"Find the derivative of f(x)=(x+4)e(5x)" was answered by our experts

Phoebe

Answered question

2021-05-11

Find the derivative of

f (x) = (x + 4) e^{(5 x)}

krolaniaN

Skilled2021-05-12Added 86 answers

Step 1
We have to find the derivative of f(x) ,where f(x) is given by

\Rightarrow \cdot f (x) = (x + 4) e^{(5 x)}

\Rightarrow \cdot f^{'} (x) =

?
Step 2
We will use following rules of derivatives.

\Rightarrow

* power rule:

\frac{d}{d x} [x^{n}] = n x^{n - 1}

\Rightarrow

* product rule:

\frac{\partial}{\partial x} (u v) = \frac{\partial u}{\partial x} v + u \frac{\partial v}{\partial x}

\Rightarrow

* Exponential rule:

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

Step 3
With the help of power rule ,chain rule and exponential rule we have solved for derivative .
Work is shown below:

\Rightarrow \cdot f (x) = (x + 4) e^{(5 x)}

\Rightarrow \cdot f^{'} (x) = e^{5 x} + 5 (x + 4) e^{5 x}

\Rightarrow \cdot f^{'} (x) = e^{5 x} (5 x + 21)

Step 4
Answer

\Rightarrow \cdot f^{'} (x) = e^{5 x} (5 x + 21)

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