Question

derivative of x cosx from first principle

Answer 1

Answer:

$-xsinx+cosx$

Step-by-step explanation:

The given equation is:

$xcosx$

Differentiating the above equation with respect to x, we have

=$x\frac{d}{dx}(cosx)+cosx\frac{d}{dx}(x)$

=$-xsinx+cosx$

Therefore, the differentiation of the given equation using the first principal, we have $-xsinx+cosx$.

Answer 2

Answer:

$\frac{d}{dx}(x\cos x)=-x\sin x+\cos x$

Step-by-step explanation:

Given : Expression $x\cos x$

To find : The derivative of given expression from first principle?

Solution :

The derivative rule of first principal is

$\frac{d}{dx}(a\cdot b)=a\times \frac{d}{dx}(b)+b\times \frac{d}{dx}(a)$

Here, a=x and b=cos x

$\frac{d}{dx}(x\cos x)=x\times \frac{d}{dx}(\cos x)+\cos x\times \frac{d}{dx}(x)$

$\frac{d}{dx}(x\cos x)=x\times (-\sin x)+\cos x\times 1$

$\frac{d}{dx}(x\cos x)=-x\sin x+\cos x$

Therefore, Derivative is $\frac{d}{dx}(x\cos x)=-x\sin x+\cos x$