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Popular >

derivative of cos(2xcos(x))

Solution

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

Solution

- 2 sin (2 x) cos (x) - sin (x) cos (2 x)

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

= - 2 sin (2 x) cos (x) - sin (x) cos (2 x)

Popular Examples

integral of (8-3x)/(sqrt(25-64x^2))

\int \frac{8 - 3 x}{25 - 64 x ^{2}} d x

derivative of (x-3)(x^2+6)derivative of

(x - 3) (x^{2} + 6)

(\partial)/(\partial x)(8xcos(x)cos(y))

\frac{\partial}{\partial x} (8 x cos (x) cos (y))

limit as x approaches 1 of (|x|)/x

x \to 1 lim (\frac{∣ x ∣}{x})

limit as x approaches 0 of h(1/x)

x \to 0 lim (h (\frac{1}{x}))

Frequently Asked Questions (FAQ)

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