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Popular >

derivative of e^{2x+5}+1/(e^{x^2})

Solution

\frac{d}{d x} (e^{2 x + 5} + \frac{1}{e ^{x^{2}}})

Solution

e^{2 x + 5} \cdot 2 - 2 e^{- x^{2}} x

Solution steps

\frac{d}{d x} (e^{2 x + 5} + \frac{1}{e ^{x^{2}}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (e^{2 x + 5}) + \frac{d}{d x} (\frac{1}{e ^{x^{2}}})

\frac{d}{d x} (e^{2 x + 5}) = e^{2 x + 5} \cdot 2

\frac{d}{d x} (\frac{1}{e ^{x^{2}}}) = - 2 e^{- x^{2}} x

= e^{2 x + 5} \cdot 2 - 2 e^{- x^{2}} x

Popular Examples

(\partial)/(\partial x)(7xcos(5xy))

\frac{\partial}{\partial x} (7 x cos (5 x y))

xyy^'=4x^2+2y^2

x y y^{^{'}} = 4 x^{2} + 2 y^{2}

derivative of x*y^2

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

laplacetransform t^{5/2}laplace transform

t^{\frac{5}{2}}

integral of x^4e^{(x^5)}

\int x^{4} e^{(x^{5})} d x

Frequently Asked Questions (FAQ)

What is the derivative of e^{2x+5}+1/(e^{x^2}) ?
The derivative of e^{2x+5}+1/(e^{x^2}) is e^{2x+5}*2-2e^{-x^2}x
What is the first derivative of e^{2x+5}+1/(e^{x^2}) ?
The first derivative of e^{2x+5}+1/(e^{x^2}) is e^{2x+5}*2-2e^{-x^2}x