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Popular >

derivative of xsin(xcos(x))

Solution

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

Solution

sin (x) cos (x) + x cos (2 x)

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

= 1 \cdot sin (x) cos (x) + cos (2 x) x

Simplify

= sin (x) cos (x) + x cos (2 x)

Popular Examples

integral of x^{10}

\int x^{10} d x

integral from 0 to 2 of e^{-3x}

\int_{0}^{2} e^{- 3 x} d x

y^{''}+y^'-6y=6t-7-(20te^{2t}+14e^{2t})

y^{^{''}} + y^{^{'}} - 6 y = 6 t - 7 - (20 t e^{2 t} + 14 e^{2 t})

tangent of f(x)=x^6,\at x=2 tangent of

f (x) = x^{6}, at x = 2

\frac{d y}{d x} = 1 + x y

Frequently Asked Questions (FAQ)

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