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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

y^{^{'}} = - 4 x y

\frac{\partial}{\partial x} (\frac{x y}{x + 7})

\int arcsec (x) d x

3^{x}

f (x) = sin (sin (x)), at x = 2 π, 0

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