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Popular >

derivative of 3cos(x-cos(3x))

Solution

\frac{d}{d x} (3 cos (x) - cos (3 x))

Solution

- 3 sin (x) + 3 sin (3 x)

Solution steps

\frac{d}{d x} (3 cos (x) - cos (3 x))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (3 cos (x)) - \frac{d}{d x} (cos (3 x))

\frac{d}{d x} (3 cos (x)) = - 3 sin (x)

\frac{d}{d x} (cos (3 x)) = - sin (3 x) \cdot 3

= - 3 sin (x) - (- sin (3 x) \cdot 3)

Simplify

= - 3 sin (x) + 3 sin (3 x)

Popular Examples

derivative of x^{2pi}

\frac{d}{d x} (x^{2 π})

integral of (2cos(x/2)-3cos(x/3))^2

\int (2 cos (\frac{x}{2}) - 3 cos (\frac{x}{3}))^{2} d x

derivative of 5/(x^2-2)

\frac{d}{d x} (\frac{5}{x ^{2} - 2})

integral of v^{-2}(2v^4+3v^2-2v^{-3})

\int v^{- 2} (2 v^{4} + 3 v^{2} - 2 v^{- 3}) d v

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

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

Frequently Asked Questions (FAQ)

What is the derivative of 3cos(x-cos(3x)) ?
The derivative of 3cos(x-cos(3x)) is -3sin(x)+3sin(3x)
What is the first derivative of 3cos(x-cos(3x)) ?
The first derivative of 3cos(x-cos(3x)) is -3sin(x)+3sin(3x)