Solve f(sqrt[5]{-243/32})^2

$$f ( \sqrt[ 5 ] { - \frac { 243 } { 32 } } ) ^ { 2 }$$

Evaluate

$$\frac{9f}{4}$$

Solution Steps

Calculate \sqrt[5]{-\frac{243}{32}} and get -\frac{3}{2}.

$$f\left(-\frac{3}{2}\right)^{2}$$

Calculate -\frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$f\times \frac{9}{4}$$

Differentiate w.r.t. f

$$\frac{9}{4} = 2\frac{1}{4} = 2.25$$

Steps Using Definition of a Derivative

Calculate \sqrt[5]{-\frac{243}{32}} and get -\frac{3}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f\left(-\frac{3}{2}\right)^{2})$$

Calculate -\frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f\times \frac{9}{4})$$

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

$$\frac{9}{4}f^{1-1}$$

Subtract 1 from 1.

$$\frac{9}{4}f^{0}$$

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

$$\frac{9}{4}\times 1$$

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

$$\frac{9}{4}$$