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Popular >

derivative of 4cos(x+4xsin(x))

Solution

\frac{d}{d x} (4 cos (x) + 4 x sin (x))

Solution

4 x cos (x)

Solution steps

\frac{d}{d x} (4 cos (x) + 4 x sin (x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (4 cos (x)) + \frac{d}{d x} (4 x sin (x))

\frac{d}{d x} (4 cos (x)) = - 4 sin (x)

\frac{d}{d x} (4 x sin (x)) = 4 (sin (x) + x cos (x))

= - 4 sin (x) + 4 (sin (x) + x cos (x))

Simplify

- 4 sin (x) + 4 (sin (x) + x cos (x)) : 4 x cos (x)

= 4 x cos (x)

Popular Examples

derivative of (sin(12x)/(e^{7x)})

\frac{d}{d x} (\frac{sin ( 12 x )}{e ^{7 x}})

integral from 0 to pi/6 of 4sec^3(x)

\int_{0}^{\frac{π}{6}} 4 sec^{3} (x) d x

(d^3)/(dx^3)(1/(x-1))

\frac{d ^{3}}{d x ^{3}} (\frac{1}{x - 1})

integral of 16tan^4(x)sec^6(x)

\int 16 tan^{4} (x) sec^{6} (x) d x

integral of \sqrt[3]{x^{-2}}

Frequently Asked Questions (FAQ)

What is the derivative of 4cos(x+4xsin(x)) ?
The derivative of 4cos(x+4xsin(x)) is 4xcos(x)
What is the first derivative of 4cos(x+4xsin(x)) ?
The first derivative of 4cos(x+4xsin(x)) is 4xcos(x)