How do you differentiate d/dx 5^2x^2?

Apr 25, 2015

In genera; an expression of the form $a {x}^{b}$ can be differentiated (with respect to $x$) as $\left(b \cdot a\right) {x}^{b - 1}$

$\frac{d {5}^{2} {x}^{2}}{\mathrm{dx}} = \left(2 \cdot {5}^{2}\right) x = 50 x$
or to phrase it another way the derivative of ${5}^{2} {x}^{2} \text{ is } 50 x$
and that is (probably?) what you want...

...if you really wanted the derivative of $\frac{d {5}^{2} {x}^{2}}{\mathrm{dx}}$
then you are asking for the second derivative:
$\frac{d \frac{d {5}^{2} {x}^{2}}{\mathrm{dx}}}{\mathrm{dx}} = 50$

Apr 27, 2015

50x

$\textcolor{g r e e n}{S o l u t i o n}$

$\frac{d}{\mathrm{dx}} {5}^{2} {x}^{2}$

Bring the constant $\textcolor{b l u e}{{5}^{2}}$ outside the $\frac{d}{\mathrm{dx}}$

So,

$= {5}^{2} \frac{d}{\mathrm{dx}} {x}^{2}$

$= 25 \left(2 x\right)$

$= 50 x$