What is the derivative of sin(x²+1)according to x?

Question

2204 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-03-12T03:22:35

$2x*cos(x^2 +1)$

Inside of our $sin(x)$ function is another function " $x^2 +1$ " so we have to use the chain rule.

The derivative of the inside function $x^2 +1$ is $2x$
( $x^2$ becomes $2x^(2-1)$ according to the power rule, 1 becomes 0 as it is a constant)

Now applying the chain rule (leaving the inside function unchanged):

$2x*d/dx(sin(x))$

The derivative of $sin(x)$ is $cos(x)$ , so we find

$d/dx(sin(x^2+1))$ =

$2x*cos(x^2+1)$