# How do you find the derivative of C=7/4x+8x²?

$\frac{\mathrm{dC}}{\mathrm{dx}} = \frac{7}{4} + 16 x$

#### Explanation:

Given function:

$C = \frac{7}{4} x + 8 {x}^{2}$

differentiating above function $C$ w.r.t. $x$ as follows

$\frac{\mathrm{dC}}{\mathrm{dx}} = \frac{d}{\mathrm{dx}} \left(\frac{7}{4} x + 8 {x}^{2}\right)$

$= \frac{7}{4} \frac{d}{\mathrm{dx}} \left(x\right) + 8 \frac{d}{\mathrm{dx}} \left({x}^{2}\right)$

$= \frac{7}{4} \left(1\right) + 8 \left(2 x\right)$

$= \frac{7}{4} + 16 x$

Jul 21, 2018

$16 x + \frac{7}{4}$

#### Explanation:

We essentially are trying to find

$\frac{d}{\mathrm{dx}} \left(8 {x}^{2} + \frac{7}{4} x\right)$

We can use the Power Rule: The exponent is multiplied by the coefficient, and the power is decremented by one. We get

$C ' = 16 x + \frac{7}{4}$

Hope this helps!