Question

find derivatives of x²+2sinx​

Answer 1

Answer:

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

Step-by-step explanation:

We have the function

$f(x)= x^2+2\sin(x)$

We know the derivative of basic functions,

$\dfrac{d}{dx}x^n =nx^{n-1}\\\\ \dfrac{d}{dx}\xin(x)=\cos(x)$

Also the algebra of derivatives,

$\dfrac{d}{dx}(cf(x)) = c \dfrac{d}{dx}f(x)\\\\\dfrac{d}{dx}(f(x)+g(x)) = \dfrac{d}{dx}f(x)+\dfrac{d}{dx}g(x)$

Using the above results, we have

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

So the derivative is $2(x+\cos(x))$

Answer 2

Answer:

2x+2cosx

hope it helps u.