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Popular >

derivative of 6e^{5x}+e^{-x^2}

Solution

\frac{d}{d x} (6 e^{5 x} + e^{- x^{2}})

Solution

30 e^{5 x} - 2 e^{- x^{2}} x

Solution steps

\frac{d}{d x} (6 e^{5 x} + e^{- x^{2}})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (6 e^{5 x}) + \frac{d}{d x} (e^{- x^{2}})

\frac{d}{d x} (6 e^{5 x}) = 30 e^{5 x}

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

= 30 e^{5 x} - 2 e^{- x^{2}} x

Popular Examples

area x^2,4x-x^2 area

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integral of 1/(25e^{-4x)+e^{4x}}

\int \frac{1}{25 e ^{- 4 x} + e ^{4 x}} d x

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\int \frac{1}{- x - 1} d x

(\partial)/(\partial x)(2(x-y)e^{2y+5x^2})

\frac{\partial}{\partial x} (2 (x - y) e^{2 y + 5 x^{2}})

Frequently Asked Questions (FAQ)

What is the derivative of 6e^{5x}+e^{-x^2} ?
The derivative of 6e^{5x}+e^{-x^2} is 30e^{5x}-2e^{-x^2}x
What is the first derivative of 6e^{5x}+e^{-x^2} ?
The first derivative of 6e^{5x}+e^{-x^2} is 30e^{5x}-2e^{-x^2}x