Evaluate the following derivatives. ddx((x+1)2x)

Question

toroztatG · Accepted Answer

Step 1
To Determine: Evaluate the following derivatives.
Given: we have a function ${(x + 1)}^{2} x$
Explanation, we have a function $y = {(x + 1)}^{2} x$ we have to find the derivative of y now we will applying exponent rule $a^{b} = e^{b \ln (a)} s o w e h a v e {(x + 1)}^{2} x = e^{2 x \ln (x + 1)}$ now we will applying the chain rule
$\frac{d}{d x} (e^{2 x \ln (x + 1)}) = e^{2 x \ln (x + 1)} \frac{d}{d x} (2 x \ln (x + 1))$
Step 2
Now we will use product rule
$e^{2 x \ln (x + 1)} \frac{d}{d x} (2 x \ln (x + 1)) = e^{2 x \ln (x + 1)} \times 2 \times [x \frac{d}{d x} \ln (x + 1) + \ln (x + 1) \frac{d x}{d x}]$
$= 2 e^{2 x \ln (x + 1)} [\frac{x}{x + 1} + \ln (x + 1)]$
$= 2 {(x + 1)}^{2 x} [\frac{x}{x + 1} + \ln (x + 1)]$

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

Evaluate the following derivatives. d/(dx)((x+1)^(2x))

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Answer & Explanation

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