Solve 25/100quadtext{(b)}37/100

$$\frac { 25 } { 100 } \quad \text { (b) } \frac { 37 } { 100 }$$

Evaluate

$$\frac{37b}{400}$$

Solution Steps

Reduce the fraction \frac{25}{100} to lowest terms by extracting and canceling out 25.

$$\frac{1}{4}b\times \frac{37}{100}$$

Multiply \frac{1}{4} times \frac{37}{100} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 37}{4\times 100}b$$

Do the multiplications in the fraction \frac{1\times 37}{4\times 100}.

$$\frac{37}{400}b$$

Differentiate w.r.t. b

$$\frac{37}{400} = 0.0925$$

Steps Using Definition of a Derivative

Reduce the fraction \frac{25}{100} to lowest terms by extracting and canceling out 25.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{1}{4}b\times \frac{37}{100})$$

Multiply \frac{1}{4} times \frac{37}{100} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{1\times 37}{4\times 100}b)$$

Do the multiplications in the fraction \frac{1\times 37}{4\times 100}.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{37}{400}b)$$

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

$$\frac{37}{400}b^{1-1}$$

Subtract 1 from 1.

$$\frac{37}{400}b^{0}$$

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

$$\frac{37}{400}\times 1$$

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

$$\frac{37}{400}$$