The second derivative is derivative which we get after differentiating the given function twice. If y is the given function with respect to variable x. Then its second derivative is denoted as F'' given as Second Derivative Calculator gives the second derivative of any given function if we enter the function in the block provided. It is amazing online tool which makes your calculation easier.

Second Derivative Examples

Steps for solving the second derivative of the given function:
1. Read the given problem and observe the given function
2. Differentiate the function two times with respect to the given variable and get the answer.

There are some solved problems given below on second derivative which will be helpful for you.

Solved Examples

Question 1: Find the second derivative of the function y = x3 + 2x - 6
Solution:

Step 1 : The given function is y = x3 + 2x - 6
Step 2 : Differentiate the given function w.r.to x, we get  $\frac{dy}{dx}$ = 3x2 + 2
Again differentiate the given function to get $\frac{d^{2}y}{dx^{2}}$ = 6x.

Question 2: Find the second derivative of function y = sin x - cos x
Solution:

Step 1 : The given function is y = sin x - cos x

Step 2 : Differentiate the given function w.r.to x, we get
$\frac{dy}{dx}$ = cos x - (- sin x) = cos x + sin x
Again differentiate the given function to get
$\frac{d^{2}y}{dx^{2}}$ = $\frac{d(cos x + sin x)}{dx}$
= cos x - sin x.

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