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Popular >

derivative of 2sin(x+4cos(x)sin(x))

Solution

\frac{d}{d x} (2 sin (x) + 4 cos (x) sin (x))

Solution

2 cos (x) + 4 cos (2 x)

Solution steps

\frac{d}{d x} (2 sin (x) + 4 cos (x) sin (x))

Simplify

2 sin (x) + 4 cos (x) sin (x) : 2 sin (x) + 2 sin (2 x)

= \frac{d}{d x} (2 sin (x) + 2 sin (2 x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (2 sin (x)) + \frac{d}{d x} (2 sin (2 x))

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

\frac{d}{d x} (2 sin (2 x)) = 4 cos (2 x)

= 2 cos (x) + 4 cos (2 x)

Popular Examples

integral of 1/((x^2)*sqrt(25x^2+16))

\int \frac{1}{( x ^{2} ) \cdot 25 x ^{2} + 16} d x

(\partial)/(\partial y)(xy+1)

\frac{\partial}{\partial y} (x y + 1)

integral of 1/((x^3-8)^2)

\int \frac{1}{( x ^{3} - 8 ) ^{2}} d x

integral of (sqrt(y^2-25))/y

\int \frac{y ^{2} - 25}{y} d y

limit as x approaches 2-of 1/(x^3-2x^2)

x \to 2 - lim (\frac{1}{x ^{3} - 2 x ^{2}})

Frequently Asked Questions (FAQ)

What is the derivative of 2sin(x+4cos(x)sin(x)) ?
The derivative of 2sin(x+4cos(x)sin(x)) is 2cos(x)+4cos(2x)
What is the first derivative of 2sin(x+4cos(x)sin(x)) ?
The first derivative of 2sin(x+4cos(x)sin(x)) is 2cos(x)+4cos(2x)