Solve f(-8)(45)(1/8)

$$f ( - 8 ) ( 45 ) ( \frac { 1 } { 8 } )$$

Evaluate

$$-45f$$

Solution Steps

Multiply -8 and 45 to get -360.

$$f\left(-360\right)\times \frac{1}{8}$$

Multiply -360 and \frac{1}{8} to get \frac{-360}{8}.

$$f\times \frac{-360}{8}$$

Divide -360 by 8 to get -45.

$$f\left(-45\right)$$

Differentiate w.r.t. f

$$-45$$

Steps Using Definition of a Derivative

Multiply -8 and 45 to get -360.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f\left(-360\right)\times \frac{1}{8})$$

Multiply -360 and \frac{1}{8} to get \frac{-360}{8}.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f\times \frac{-360}{8})$$

Divide -360 by 8 to get -45.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f\left(-45\right))$$

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

$$-45f^{1-1}$$

Subtract 1 from 1.

$$-45f^{0}$$

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

$$-45$$