Solve -8*f(0)+4*g(-8)=

$$- 8 \cdot f ( 0 ) + 4 \cdot g ( - 8 ) =$$

Evaluate

$$-32g$$

Solution Steps

Multiply -8 and 0 to get 0.

$$0f+4g\left(-8\right)$$

Anything times zero gives zero.

$$0+4g\left(-8\right)$$

Multiply 4 and -8 to get -32.

$$0-32g$$

Anything plus zero gives itself.

$$-32g$$

Differentiate w.r.t. g

$$-32$$

Steps Using Definition of a Derivative

Multiply -8 and 0 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}g}(0f+4g\left(-8\right))$$

Anything times zero gives zero.

$$\frac{\mathrm{d}}{\mathrm{d}g}(0+4g\left(-8\right))$$

Multiply 4 and -8 to get -32.

$$\frac{\mathrm{d}}{\mathrm{d}g}(0-32g)$$

Anything plus zero gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}g}(-32g)$$

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

$$-32g^{1-1}$$

Subtract 1 from 1.

$$-32g^{0}$$

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

$$-32$$