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

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

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

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

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

- 5 sin (x) + 5 sin (5 x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

= - 5 sin (x) + 5 sin (5 x)

\int \frac{3 x ^{2} - x + 1}{x ^{3} - x ^{2}} d x

y^{^{''}} + 49 y = cos (10 t)

ln (x^{3} + 5 x + 3)

x \to 1 lim (x sin (\frac{1}{x}))

y = x^{4} - 3 x^{2} + 2, (1, 0)

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