Derivatives Evaluate the following derivatives. ddx((2x)4x)

Stacie Worsley

Stacie Worsley

Answered

2022-01-14

Derivatives Evaluate the following derivatives.
ddx((2x)4x)

Answer & Explanation

Ethan Sanders

Ethan Sanders

Expert

2022-01-15Added 35 answers

Step 1
Given,
ddx[(2x)4x]
Step 2
Given equation can be written as
ddx[(2x)4x]=2ddx[(x)4x]
We can write x4x as follows
x4x=eln(x4x)
=e4xln(x)
Hence
ddx[(2x)4x]=2ddx[e4xln(x)]
We apply the chain rule
ddx[(2x)4x]=2[e4xln(x)]ddx[4xln(x)]
=2[e4xln(x)]4[x×1x+ln(x)]
=2[e4xln(x)][1+ln(x)]
=2x4x[1+ln(x)]
Neunassauk8

Neunassauk8

Expert

2022-01-16Added 30 answers

((2x)4x)=((eln2x)4x) [2x=eln2x]
=(e4xln2x) [Power rule]
=e4xln2x(4xln2x) [Chain rule]
=e4xln2x(4ln2x+4x12x2) [Product rule + chain rule]
=(2x)4x(4ln2x+4)
Result:
(2x)4x(4ln2x+4)

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