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Popular >

derivative of cos(x*sin(x))

Solution

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

Solution

cos (2 x)

Solution steps

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

Apply the Product Rule:

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

f = cos (x), g = sin (x)

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

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

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

= (- sin (x)) sin (x) + cos (x) cos (x)

Simplify

(- sin (x)) sin (x) + cos (x) cos (x) : cos (2 x)

= cos (2 x)

Graph

Popular Examples

y^{''}+9y=xe^{2x}

y^{^{''}} + 9 y = x e^{2 x}

(\partial)/(\partial x)(3/((x^2+z^2)))

\frac{\partial}{\partial x} (\frac{3}{( x ^{2} + z ^{2} )})

integral of (ln^3(x))/(xsqrt(ln^2(x)-4))

\int \frac{ln ^{3} ( x )}{x ln ^{2} ( x ) - 4} d x

integral of (csc^2(x))/(cot(x))

\int \frac{csc ^{2} ( x )}{cot ( x )} d x

\frac{d}{d z} (x e^{z})

Frequently Asked Questions (FAQ)

What is the derivative of cos(x*sin(x)) ?
The derivative of cos(x*sin(x)) is cos(2x)
What is the first derivative of cos(x*sin(x)) ?
The first derivative of cos(x*sin(x)) is cos(2x)