Get the solution to "If f is a differentiable function, find an..." - Plainmath

Jaden Easton

Answered question

2021-10-15

If f is a differentiable function, find an expression for the derivative of:

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

Answer & Explanation

hosentak

Skilled2021-10-16Added 100 answers

Step 1
given that

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

differentiatee on both side
we apply division rulee here
Step 2

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

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

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

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