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Popular >

(\partial)/(\partial x)(xcos(x)sin(x))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{\partial}{\partial x} (x) = 1

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

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

Simplify

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

Popular Examples

derivative of f(x)=cos(x)sec(x)derivative of

f (x) = cos (x) sec (x)

derivative of x^2-5 derivative of

x^{2} - 5

derivative of (2x^{3x})

\frac{d}{d x} ((2 x)^{3 x})

derivative of 5x-9

\frac{d}{d x} (5 x - 9)

y^{''}-5y^'+6y=sin(x)

y^{^{''}} - 5 y^{^{'}} + 6 y = sin (x)

Frequently Asked Questions (FAQ)

What is (\partial)/(\partial x)(xcos(x)sin(x)) ?
The answer to (\partial)/(\partial x)(xcos(x)sin(x)) is cos(x)sin(x)+xcos(2x)