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Popular >

derivative of-cos(xsin(x))

Solution

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

Solution

- cos (2 x)

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - \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

(\partial)/(\partial x)(4xy)

\frac{\partial}{\partial x} (4 x y)

integral of e^{2x}cos(2x)

\int e^{2 x} cos (2 x) d x

derivative of arctanh(sin(x))

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

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

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

integral of (4x^2-3cos(x))

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

Frequently Asked Questions (FAQ)

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