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derivative of cos(x+x^2sin(x))

Solution

\frac{d}{d x} (cos (x) + x^{2} sin (x))

Solution

- sin (x) + 2 x sin (x) + cos (x) x^{2}

Solution steps

\frac{d}{d x} (cos (x) + x^{2} sin (x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (cos (x)) + \frac{d}{d x} (x^{2} sin (x))

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

\frac{d}{d x} (x^{2} sin (x)) = 2 x sin (x) + cos (x) x^{2}

= - sin (x) + 2 x sin (x) + cos (x) x^{2}

Popular Examples

(\partial)/(\partial y)(xe^{5y})

\frac{\partial}{\partial y} (x e^{5 y})

derivative of (cos(x+2)^3(2x)^{-3x})

\frac{d}{d x} ((cos (x) + 2)^{3} (2 x)^{- 3 x})

sum from n=1 to infinity of ((-1)^nx^n)/(\sqrt[3]{n)}

derivative of f(x)= 9/(x^3)derivative of

f (x) = \frac{9}{x ^{3}}

integral of sec^2(x)tan^3(x)

\int sec^{2} (x) tan^{3} (x) d x

Frequently Asked Questions (FAQ)

What is the derivative of cos(x+x^2sin(x)) ?
The derivative of cos(x+x^2sin(x)) is -sin(x)+2xsin(x)+cos(x)x^2
What is the first derivative of cos(x+x^2sin(x)) ?
The first derivative of cos(x+x^2sin(x)) is -sin(x)+2xsin(x)+cos(x)x^2