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Popular >

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

Popular Examples

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

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

(\partial)/(\partial x)(x^2y+xy^3)

\frac{\partial}{\partial x} (x^{2} y + x y^{3})

limit as x approaches infinity of 2/3

x \to \infty lim (\frac{2}{3})

derivative of 1+x^{3/2}

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

(\partial)/(\partial x)(7/(7x+8y))

\frac{\partial}{\partial x} (\frac{7}{7 x + 8 y})

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