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Popular Calculus >

derivative of y=e^{7x}+7xe^{7x}

Solution

derivative of

y = e^{7 x} + 7 x e^{7 x}

Solution

14 e^{7 x} + 49 e^{7 x} x

Solution steps

\frac{d}{d x} (e^{7 x} + 7 x e^{7 x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (e^{7 x}) + \frac{d}{d x} (7 x e^{7 x})

\frac{d}{d x} (e^{7 x}) = e^{7 x} \cdot 7

\frac{d}{d x} (7 x e^{7 x}) = 7 (e^{7 x} + 7 e^{7 x} x)

= e^{7 x} \cdot 7 + 7 (e^{7 x} + 7 e^{7 x} x)

Simplify

e^{7 x} \cdot 7 + 7 (e^{7 x} + 7 e^{7 x} x) : 14 e^{7 x} + 49 e^{7 x} x

= 14 e^{7 x} + 49 e^{7 x} x

Graph

Popular Examples

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t an g e n t f (x) = 6 e^{- 0.6 x}, at x = 4

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\int (y - 1) d y

(\partial)/(\partial x)(xe^{4x})

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a re a 2 x = y, x + y = 4, x + y = 12

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

Frequently Asked Questions (FAQ)

What is the derivative of y=e^{7x}+7xe^{7x} ?
The derivative of y=e^{7x}+7xe^{7x} is 14e^{7x}+49e^{7x}x
What is the first derivative of y=e^{7x}+7xe^{7x} ?
The first derivative of y=e^{7x}+7xe^{7x} is 14e^{7x}+49e^{7x}x