Question

differentiation of sin(x²+5)​

Answer 1

Answer:

The derivative of $\sin(x^2+5)$ is $2x\cos(x^2+5)$

Step-by-step explanation:

We know that,

$\dfrac{d}{dx}\sin(x)= \cos x$  .

When we have composition of two function, we use chain rule for differentiation. Here the given function is composition of the functions $\sin x$ and $x^2+5$. Thus the derivative is given by,

$\dfrac{d}{dx}\sin(x^2+5)=\cos(x^2+5) \dfrac{d}{dx}(x^2+5)\\\\=\cos(x^2+5)\times 2x = 2x\cos(x^2+5)$

Here

$\dfrac{d}{dx} x^2+5=2x$   .