What is the derivative of cos^2(xsin(x)) ?

The derivative of cos^2(xsin(x)) is -2cos(x)+3cos^3(x)

What is the first derivative of cos^2(xsin(x)) ?

The first derivative of cos^2(xsin(x)) is -2cos(x)+3cos^3(x)

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = cos^{2} (x), g = sin (x)

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

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

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

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

Simplify

(- sin (2 x)) sin (x) + cos (x) cos^{2} (x) : - 2 cos (x) + 3 cos^{3} (x)

= - 2 cos (x) + 3 cos^{3} (x)

(x^{3} + 5) e x

\int \frac{x ^{4}}{x + 4} d x

\frac{\partial}{\partial z} (\frac{e ^{x z + y}}{z ^{2} + w})

sin (t)

\int ln (x^{3}) d x

What is the derivative of cos^2(xsin(x)) ?
The derivative of cos^2(xsin(x)) is -2cos(x)+3cos^3(x)
What is the first derivative of cos^2(xsin(x)) ?
The first derivative of cos^2(xsin(x)) is -2cos(x)+3cos^3(x)