Zoe Oneal

2021-05-29

Let f and g be differentiable functions. Find a formula for $\frac{d}{dx}\left[\frac{3f\left(x\right)}{2}-5g\left(x\right)\right]$

avortarF

Step 1
Derivative of f(x) is f'(x).
Derivative of g(x) is g'(x).
Step 2
$\frac{d}{dx}\left[\frac{3f\left(x\right)}{2}-5g\left(x\right)\right]$
$=\frac{d}{dx}\left[\frac{3f\left(x\right)}{2}\right]-\frac{d}{dx}\left[5g\left(x\right)\right]$
$=\frac{3}{2}\frac{d}{dx}\left[f\left(x\right)\right]-5\frac{d}{dx}\left[g\left(x\right)\right]$
$=\frac{3}{2}{f}^{\prime }\left(x\right)-5{g}^{\prime }\left(x\right)$
Answer:$\frac{3}{2}{f}^{\prime }\left(x\right)-5{g}^{\prime }\left(x\right)$

Jeffrey Jordon