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Popular >

derivative of e^xsin(e^x)

Solution

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

Solution

e^{x} sin (e^{x}) + e^{2 x} cos (e^{x})

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x}, g = sin (e^{x})

= \frac{d}{d x} (e^{x}) sin (e^{x}) + \frac{d}{d x} (sin (e^{x})) e^{x}

\frac{d}{d x} (e^{x}) = e^{x}

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

= e^{x} sin (e^{x}) + cos (e^{x}) e^{x} e^{x}

cos (e^{x}) e^{x} e^{x} = e^{2 x} cos (e^{x})

= e^{x} sin (e^{x}) + e^{2 x} cos (e^{x})

Popular Examples

derivative of x^2+xy

\frac{d}{d x} (x^{2} + x y)

d/(dt)(e^{3cos(t)+2t^2})

\frac{d}{d t} (e^{3 c o s (t) + 2 t^{2}})

(\partial)/(\partial x)(e^{-9x^2-2y^2})

\frac{\partial}{\partial x} (e^{- 9 x^{2} - 2 y^{2}})

integral of sec^2(2xy)

\int sec^{2} (2 x y) d x

derivative of (x^2-8x+7/(x^2+9))

\frac{d}{d x} (\frac{x ^{2} - 8 x + 7}{x ^{2} + 9})

Frequently Asked Questions (FAQ)

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