Solve 9/2quadtext{(d)}17/2

$$\frac { 9 } { 2 } \quad \text { (d) } \frac { 17 } { 2 }$$

Evaluate

$$\frac{153d}{4}$$

Solution Steps

Multiply \frac{9}{2} times \frac{17}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 17}{2\times 2}d$$

Do the multiplications in the fraction \frac{9\times 17}{2\times 2}.

$$\frac{153}{4}d$$

Differentiate w.r.t. d

$$\frac{153}{4} = 38\frac{1}{4} = 38.25$$

Steps Using Definition of a Derivative

Multiply \frac{9}{2} times \frac{17}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{9\times 17}{2\times 2}d)$$

Do the multiplications in the fraction \frac{9\times 17}{2\times 2}.

$$\frac{\mathrm{d}}{\mathrm{d}d}(\frac{153}{4}d)$$

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

$$\frac{153}{4}d^{1-1}$$

Subtract 1 from 1.

$$\frac{153}{4}d^{0}$$

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

$$\frac{153}{4}\times 1$$

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

$$\frac{153}{4}$$