"Find the derivatives of the functions y=x94+e−2x" was answered by students like you

College
Calculus and Analysis
Differential Calculus
Derivatives

nagasenaz

Answered question

2021-10-19

Find the derivatives of the functions

y = x \frac{9}{4} + e^{- 2 x}

Answer & Explanation

Nathalie Redfern

Skilled2021-10-20Added 99 answers

Given,
$y = x \frac{9}{4} + e^{- 2 x}$
Differentiating with respect to x, we get
$\frac{d y}{d x} = \frac{9}{4} \cdot x^{\frac{9}{4} - 1} + e^{- 2 x} \cdot \frac{d (- 2 x)}{d x}$

$[∵ \frac{d (x^{n})}{d x} = n x^{n - 1}; \frac{d (e^{x})}{d x} = e^{x}]$
$\Rightarrow \frac{d y}{d x} = \frac{9}{4} \cdot x^{\frac{5}{4}} + e^{- 2 x} \cdot (- 2)$
$\Rightarrow \frac{d y}{d x} = \frac{9}{4} \cdot x^{\frac{5}{4}} - 2 e^{- 2 x}$

Jeffrey Jordon

Expert2022-11-14Added 2605 answers

Answer is given below (on video)

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