Solve sqrt[5]{-243/3125}F(25/-1)

$$\sqrt[ 5 ] { \frac { - 243 } { 3125 } } F ( \frac { 25 } { - 1 } )$$

Evaluate

$$15F$$

Solution Steps

Fraction \frac{-243}{3125} can be rewritten as -\frac{243}{3125} by extracting the negative sign.

$$\sqrt[5]{-\frac{243}{3125}}F\times \frac{25}{-1}$$

Calculate \sqrt[5]{-\frac{243}{3125}} and get -\frac{3}{5}.

$$-\frac{3}{5}F\times \frac{25}{-1}$$

Fraction \frac{25}{-1} can be rewritten as -25 by extracting the negative sign.

$$-\frac{3}{5}F\left(-25\right)$$

Multiply -\frac{3}{5} and -25 to get 15.

$$15F$$

Differentiate w.r.t. F

$$15$$

Steps Using Definition of a Derivative

Fraction \frac{-243}{3125} can be rewritten as -\frac{243}{3125} by extracting the negative sign.

$$\frac{\mathrm{d}}{\mathrm{d}F}(\sqrt[5]{-\frac{243}{3125}}F\times \frac{25}{-1})$$

Calculate \sqrt[5]{-\frac{243}{3125}} and get -\frac{3}{5}.

$$\frac{\mathrm{d}}{\mathrm{d}F}(-\frac{3}{5}F\times \frac{25}{-1})$$

Fraction \frac{25}{-1} can be rewritten as -25 by extracting the negative sign.

$$\frac{\mathrm{d}}{\mathrm{d}F}(-\frac{3}{5}F\left(-25\right))$$

Multiply -\frac{3}{5} and -25 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}F}(15F)$$

The derivative of ax^{n} is nax^{n-1}.

$$15F^{1-1}$$

Subtract 1 from 1.

$$15F^{0}$$

For any term t except 0, t^{0}=1.

$$15\times 1$$

For any term t, t\times 1=t and 1t=t.

$$15$$