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

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derivative of

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

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

f (x) = 6 e^{- 0.6 x}, at x = 4

\int (y - 1) d y

\int - 0.5 y d y

\frac{\partial}{\partial x} (x e^{4 x})

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