What is the derivative of 5sin(x-sin(5x)) ?

The derivative of 5sin(x-sin(5x)) is 5cos(x)-cos(5x)*5

What is the first derivative of 5sin(x-sin(5x)) ?

The first derivative of 5sin(x-sin(5x)) is 5cos(x)-cos(5x)*5

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

5 cos (x) - cos (5 x) \cdot 5

Solution steps

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

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (5 sin (x)) - \frac{d}{d x} (sin (5 x))

\frac{d}{d x} (5 sin (x)) = 5 cos (x)

\frac{d}{d x} (sin (5 x)) = cos (5 x) \cdot 5

= 5 cos (x) - cos (5 x) \cdot 5

\frac{e ^{- 6 s}}{s ^{2} + 2 s - 8}

\int \frac{4 x + x ^{2}}{x ^{2}} d x

\frac{\partial}{\partial x} (x yz - z - sin (x + y))

f (x) = ln (\frac{x - 2}{x + 1})

\int x (7 - y)

What is the derivative of 5sin(x-sin(5x)) ?
The derivative of 5sin(x-sin(5x)) is 5cos(x)-cos(5x)*5
What is the first derivative of 5sin(x-sin(5x)) ?
The first derivative of 5sin(x-sin(5x)) is 5cos(x)-cos(5x)*5