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Popular >

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

Solution

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

Solution

2 cos (x) + cos (2 x) \cdot 2

Solution steps

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

Simplify

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

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

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

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

= 2 cos (x) + cos (2 x) \cdot 2

Popular Examples

derivative of 3^x derivative of

3^{x}

integral of (x^2+2)/(x^2+1)

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

integral of (sqrt(x)+1/x+sqrt(pi))

\int (x + \frac{1}{x} + π) d x

integral of 1/(x^{12)}

\int \frac{1}{x ^{12}} d x

derivative of f(x)=sqrt(x)(3x+x^2)derivative of

f (x) = x (3 x + x^{2})

Frequently Asked Questions (FAQ)

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