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sanuluy

Answered question

2021-10-16

Derivatives of Inverse Trigonometric, Logarithmic, and Exponential Functions

y = e^{x^{2} - 2 x}

Answer & Explanation

svartmaleJ

Skilled2021-10-17Added 92 answers

Step 1
The function is

y = e^{x^{2} - 2 x}

.
Differentiate the function with respect to x.

\frac{d y}{d x} = \frac{d}{d x} (e^{x^{2} - 2 x})

= e^{x^{2} - 2 x} [\frac{d}{d x} (x^{2} - 2 x)]

= e^{x^{2} - 2 x} [2 x - 2]

= 2 (x - 1) e^{x^{2} - 2 x}

Step 2
Thus, the derivative is

2 (x - 1) e^{x^{2} - 2 x}

.

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