Solve -2^4*2^3quadtext{f}quad2^4

$$- 2 ^ { 4 } \cdot 2 ^ { 3 } \quad \text { f } \quad 2 ^ { 4 }$$

Evaluate

$$-2048f$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\left(-2^{4}\right)\times 2^{7}f$$

Calculate 2 to the power of 4 and get 16.

$$-16\times 2^{7}f$$

Calculate 2 to the power of 7 and get 128.

$$-16\times 128f$$

Multiply -16 and 128 to get -2048.

$$-2048f$$

Differentiate w.r.t. f

$$-2048$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}f}(\left(-2^{4}\right)\times 2^{7}f)$$

Calculate 2 to the power of 4 and get 16.

$$\frac{\mathrm{d}}{\mathrm{d}f}(-16\times 2^{7}f)$$

Calculate 2 to the power of 7 and get 128.

$$\frac{\mathrm{d}}{\mathrm{d}f}(-16\times 128f)$$

Multiply -16 and 128 to get -2048.

$$\frac{\mathrm{d}}{\mathrm{d}f}(-2048f)$$

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

$$-2048f^{1-1}$$

Subtract 1 from 1.

$$-2048f^{0}$$

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

$$-2048$$