Solve -15*3/2b

$$- 15 \cdot \frac { 3 } { 2 } b$$

Evaluate

$$-\frac{45b}{2}$$

Solution Steps

Express -15\times \frac{3}{2} as a single fraction.

$$\frac{-15\times 3}{2}b$$

Multiply -15 and 3 to get -45.

$$\frac{-45}{2}b$$

Fraction \frac{-45}{2} can be rewritten as -\frac{45}{2} by extracting the negative sign.

$$-\frac{45}{2}b$$

Differentiate w.r.t. b

$$-\frac{45}{2} = -22\frac{1}{2} = -22.5$$

Steps Using Definition of a Derivative

Express -15\times \frac{3}{2} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{-15\times 3}{2}b)$$

Multiply -15 and 3 to get -45.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{-45}{2}b)$$

Fraction \frac{-45}{2} can be rewritten as -\frac{45}{2} by extracting the negative sign.

$$\frac{\mathrm{d}}{\mathrm{d}b}(-\frac{45}{2}b)$$

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

$$-\frac{45}{2}b^{1-1}$$

Subtract 1 from 1.

$$-\frac{45}{2}b^{0}$$

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

$$-\frac{45}{2}$$