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Popular >

derivative of sin(xcos(2x))

Solution

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

Solution

- 5 cos (x) + 6 cos^{3} (x)

Solution steps

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

Apply the Product Rule:

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

f = sin (x), g = cos (2 x)

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

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

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

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

Simplify

cos (x) cos (2 x) + (- sin (2 x) \cdot 2) sin (x) : - 5 cos (x) + 6 cos^{3} (x)

= - 5 cos (x) + 6 cos^{3} (x)

Popular Examples

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

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

integral from z-1 to 1 of 3x^2-4zx+2z^2

\int_{z - 1}^{1} 3 x^{2} - 4 z x + 2 z^{2}

derivative of ln(3x^2+4)

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

limit as x approaches-5 of (x^2-8)/(5-x)

x \to - 5 lim (\frac{x ^{2} - 8}{5 - x})

derivative of 24x^{3/2}

\frac{d}{d x} (24 x^{\frac{3}{2}})

Frequently Asked Questions (FAQ)

What is the derivative of sin(xcos(2x)) ?
The derivative of sin(xcos(2x)) is -5cos(x)+6cos^3(x)
What is the first derivative of sin(xcos(2x)) ?
The first derivative of sin(xcos(2x)) is -5cos(x)+6cos^3(x)