Resolved: "Evaluate the derivatives. R=74x−x2" - Plainmath

lwfrgin

Answered question

2021-09-28

Evaluate the derivatives.

R = 7^{4 x - x^{2}}

Answer & Explanation

Ayesha Gomez

Skilled2021-09-29Added 104 answers

Step 1
Given:

R = 7^{4 x - x^{2}}

We find derivative
Step 2
we find derivative
since

R = 7^{4 x - x^{2}}

differentiate with respect to "x", we get

\frac{d R}{d x} = \frac{d}{d x} 7^{4 x - x^{2}} ∵ \frac{d}{d x} a^{x} = a^{x} \log a

\Rightarrow \frac{d R}{d x} = 7^{4 x - x^{2}} \log (7) \cdot \frac{d}{d x} (4 x - x^{2})

= 7^{4 x - x^{2}} \log (7) (4 - 2 x)

\Rightarrow \frac{d R}{d x} = (4 - 2 x) \log (7) \cdot 7^{4 x - x^{2}}

Hence

\frac{d R}{d x} = (4 - 2 x) \log (7) 7^{4 x - x^{2}}

Jeffrey Jordon

Expert2022-02-01Added 2605 answers

Answer is given below (on video)

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