What is the derivative of sin(xcos^2(x)) ?

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

What is the first derivative of sin(xcos^2(x)) ?

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\int \frac{1}{4 - 4 sin ( x )} d x

\int 8 x^{7} e^{7 x^{8}} d x

\int \frac{- 6 x ^{3} + 8 x ^{2} - 30 x + 10}{x ^{3} + 5 x} d x

\int x^{2} + 6 d x

x ln (x)

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