Derivative Math Problems

In math, differentiation is the process of finding the derivative which means measuring how a function changes with respect to its input. The derivative of y with respect to x is given by`(dy)/(dx)` . The reverse process of derivative is antiderivative. Following is the example and practice problems of math derivative which helps you for learning derivative in math.

Example Problems of Math Derivative:

Learn math derivative with Example problem 1:

Find the derivative of the function y = 7x8 + 2x6 + 5x5

Solution:

Step 1: Given function

y = 7x8 + 2x6 + 5x5

Step 2: Differentiate the given function y = 7x8 + 2x6 + 5x5 with respect to ' x ', to get `(dy)/dx`

`(dy)/dx` = 56x7 + 12x5 + 25x4

Learn math derivative with example problem 2:

Find the derivative of the function y = sin (7x4 + 1)

Solution:

Step 1: Given function

y = sin (7x4 + 1)

Step 2: Differentiate the given function y = sin (7x4 + 1) with respect to ' x ', to get `(dy)/dx`

`(dy)/dx` = [cos(7x4 + 1)] (28x3)

= 28x3 cos (7x4 + 1)

Learn math derivative with example problem 3:

Find the derivative of the function y = ecos(9x - 14)

Solution:

Step 1: Given function

y = ecos (9x - 14)

Step 2: Differentiate the given function y =  ecos (9x - 14) with respect to ' x ', to get `(dy)/dx`

`(dy)/dx` = ecos (9x - 14) (- 9sin (9x - 14))

= - 9 ecos (9x - 14) sin (9x - 14)

Practice Problems of Math Derivative:

A few practice problems are given below with solutions which gives you idea how to differentiate the function.

1) Find the derivative of the function y = 16x2 + 11x + 5

2) Find the derivative of the function y = - 5tan (7x2 + 2)

3) Find the derivative of the function y = `6/5` e sin (5x - 9)

Solutions:

1) 32x + 11

2) - 70x sec2 (7x2 + 2)

3) 6e sin (5x - 9) cos (5x - 9)

Solving Equations with Exponents

Introduction:

Exponent equations are the equations in which variable appear as an exponent.

To solve these equations rules and laws of exponents are used. Exponent equations are of two types
(1) Exponent equations in which bases are same
(2) Exponent equations in which bases are different.

Steps to Solve Equations with Exponent

Solving Exponential Equations of the same base

1) Ignore the bases, and simply set the exponents equal to each other
2) Solve for the variable

 When the bases of the terms are different

1) Ignore the exponents; rewrite both of the bases as powers of same number.
For example if there are 2 and 4 in the bases, then convert base 4, in to base 2
by writing it again as (2)^2
2) once the bases are same , ignore them
3) Equalize the exponents
4) Solve for variable

Simple Problems of Equations with Exponents

Solve for variable Answer 1. 3m  =  35 Since the bases are the same, set the exponents equal to one another: m = 5 2. 5t   = 125 125can be expressed as a power of 5: 5t  = 53 t = 3 3.  493y=343 49 and 343 can be expressed as a power of 7: [(7)2]3y = 73 76y = 73 6y = 3 y = 1/2

More Problems of Equations with Exponents

Solve for x. Answer 1.  52x+1  =  53x-2 Since the bases are the same, set the exponents equal to one another: 2x + 1 = 3x - 2 3 = x 2.  32x-1  = 27x 27 can be expressed as a power of 3: 32x-1  = 33x 2x - 1 = 3x -1 = x 3.   43x-8  = 162x 16 can be expressed as a power of 4: 43x-8= [(4)2]2x 3x - 8 = 4x   -8 = x

Units of Meters

In this article discuss about standard units (international system) of meters. The meter (or meter), symbol m, is the base unit of length in the International System of Units (SI).The meters is the length of path travelled by light in vacuum during a time interval of 1/299792458 of a seconds.

The Basic Units of Length is Meters (m):

Linear measures     Short form of writing

Millimeter                         mm

Centimeter                         cm

Decimeter                          dm

Meter                                m

Decameter                         dam

Hectometer                         hm

Kilometer                           km

Some examples of units values:

1 mm = 0.001 m

1 cm = 0.01 m

1 dc = 0.1 m

1 km = 1000 m

Units of Meters - Examples:

Units of meters - Example 1:

Convert 378.6 cm into meter

Solution:

Here the conversion is from centimeter to meter. i.e. from lower unit to higher unit

100cm = 1m.

Hence 378.6cm = 378.6/100 m

= 3.786 m (shifting the decimal two digits to the left)

Units of meters - Example 2:

Convert 40.1735 km into meter.

Solution:

Here the conversion is from higher to lower. Hence we have to shift the decimal point to the right.

1km = 1000 m

40.1735 km = 40.1735 × 1000 m

= 40173.5 m

Units of meters - Example 3:

Convert 6m into millimeter.

Solution:

Note: Here we are converting the unit meter into millimeter. i.e. from higher unit to lower unit. So the operation should be multiplication.

1 m = 1000 mm

Hence 6 m = 6 × 1000 mm

= 6000 mm

Units of meters - Example 4:

Convert 778.6 cm into meter

Solution:

Here the conversion is from centimeter to meter. i.e. from lower unit to higher unit

100cm = 1m.

Hence 778.6cm = 778.6/100 m

= 7.786 m (shifting the decimal two digits to the left)

Units of meters - Example 5:

Convert 90.1736 km into meter.

Solution:

Here the conversion is from higher to lower. Hence we have to shift the decimal point to the right.

1km = 1000 m

90.1736 km = 90.1736 × 1000 m

= 90173.6 m

Units of meters - Example 6:

Convert 9m into millimeter.

Solution:

Note: Here we are converting the unit meter into millimeter. i.e. from higher unit to lower unit. So the operation should be multiplication.

1 m = 1000 mm

Hence 9 m = 9 × 1000 mm

= 9000 mm.