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Popular >

derivative of (1-x)cos(2x)

Solution

derivative of

(1 - x) cos (2 x)

Solution

- cos (2 x) - 2 sin (2 x) (1 - x)

Solution steps

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

Apply the Product Rule:

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

f = 1 - x, g = cos (2 x)

= \frac{d}{d x} (1 - x) cos (2 x) + \frac{d}{d x} (cos (2 x)) (1 - x)

\frac{d}{d x} (1 - x) = - 1

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

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

Simplify

= - cos (2 x) - 2 sin (2 x) (1 - x)

Popular Examples

integral of (1-1/(x^2))sqrt(x)

\int (1 - \frac{1}{x ^{2}}) x d x

derivative of (x+y/(sqrt(x^2+y^2)))

\frac{d}{d x} (\frac{x + y}{x ^{2} + y ^{2}})

laplacetransform e^{-3t}sin(2t)laplace transform

e^{- 3 t} sin (2 t)

derivative of (x^2/9)

\frac{d}{d x} (\frac{x ^{2}}{9})

y^{''}+4y=2csc^2(2t)

y^{^{''}} + 4 y = 2 csc^{2} (2 t)

Frequently Asked Questions (FAQ)

What is the derivative of (1-x)cos(2x) ?
The derivative of (1-x)cos(2x) is -cos(2x)-2sin(2x)(1-x)
What is the first derivative of (1-x)cos(2x) ?
The first derivative of (1-x)cos(2x) is -cos(2x)-2sin(2x)(1-x)