Let f and g be differentiable functions. Find a formula for ddx[3f(x)2−5g(x)]

Zoe Oneal

Answered question

2021-05-29

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

Answer & Explanation

avortarF

Skilled2021-05-30Added 113 answers

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