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Popular Calculus >

derivative of 3sin(xcos(x))

Solution

\frac{d}{d x} (3 sin (x) cos (x))

Solution

3 cos (2 x)

Solution steps

\frac{d}{d x} (3 sin (x) cos (x))

Take the constant out:

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

= 3 \frac{d}{d x} (sin (x) cos (x))

Apply the Product Rule:

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

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

= 3 (\frac{d}{d x} (sin (x)) cos (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)

= 3 (cos (x) cos (x) + (- sin (x)) sin (x))

Simplify

3 (cos (x) cos (x) + (- sin (x)) sin (x)) : 3 cos (2 x)

= 3 cos (2 x)

Graph

Popular Examples

derivative of f(x)=x^{-1}-1/x

d er i v a t i v e f (x) = x^{- 1} - \frac{1}{x}

derivative of 2/(3x-1)

\frac{d}{d x} (\frac{2}{3 x - 1})

integral of y^2cos(x)+z^3

\int y^{2} cos (x) + z^{3} d x

f^{''}(x)=4x^2+8x-17

f^{^{''}} (x) = 4 x^{2} + 8 x - 17

(\partial)/(\partial x)(4x^2+5y^3-3)

\frac{\partial}{\partial x} (4 x^{2} + 5 y^{3} - 3)

Frequently Asked Questions (FAQ)

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