Solve f(81/16)^-frac{3{4}}

$$f ( \frac { 81 } { 16 } ) ^ { - \frac { 3 } { 4 } }$$

Differentiate w.r.t. f

$$\frac{8}{27} = 0.2962962962962963$$

Steps Using Definition of a Derivative

Calculate \frac{81}{16} to the power of -\frac{3}{4} and get \frac{8}{27}.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f\times \frac{8}{27})$$

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

$$\frac{8}{27}f^{1-1}$$

Subtract 1 from 1.

$$\frac{8}{27}f^{0}$$

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

$$\frac{8}{27}\times 1$$

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

$$\frac{8}{27}$$

Evaluate

$$\frac{8f}{27}$$

Solution Steps

Calculate \frac{81}{16} to the power of -\frac{3}{4} and get \frac{8}{27}.

$$f\times \frac{8}{27}$$