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)