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Popular Calculus >

derivative of e^{sin(2x}+sin(e^{2x}))

Solution

\frac{d}{d x} (e^{s i n (2 x)} + sin (e^{2 x}))

Solution

e^{s i n (2 x)} cos (2 x) \cdot 2 + cos (e^{2 x}) e^{2 x} \cdot 2

Solution steps

\frac{d}{d x} (e^{s i n (2 x)} + sin (e^{2 x}))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (e^{s i n (2 x)}) + \frac{d}{d x} (sin (e^{2 x}))

\frac{d}{d x} (e^{s i n (2 x)}) = e^{s i n (2 x)} cos (2 x) \cdot 2

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

= e^{s i n (2 x)} cos (2 x) \cdot 2 + cos (e^{2 x}) e^{2 x} \cdot 2

Graph

Popular Examples

derivative of f(x)=(cos(x)-4)/(2sin(x))

d er i v a t i v e f (x) = \frac{cos ( x ) - 4}{2 sin ( x )}

derivative of (x^4+3x^2(1-5x))

\frac{d}{d x} ((x^{4} + 3 x^{2}) (1 - 5 x))

integral of e^{-bx}

\int e^{- b x} d x

integral from 1 to 3 of x^2ln(x)

\int_{1}^{3} x^{2} ln (x) d x

integral of (5x^2+2x-5)/(x^3-x)

\int \frac{5 x ^{2} + 2 x - 5}{x ^{3} - x} d x

Frequently Asked Questions (FAQ)

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