Solve 24a^4/b^3b^4/8a^4

$$\frac { 24 a ^ { 4 } } { b ^ { 3 } } \frac { b ^ { 4 } } { 8 a ^ { 4 } }$$

Evaluate

$$3b$$

Solution Steps

Multiply \frac{24a^{4}}{b^{3}} times \frac{b^{4}}{8a^{4}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{24a^{4}b^{4}}{b^{3}\times 8a^{4}}$$

Cancel out 8b^{3}a^{4} in both numerator and denominator.

$$3b$$

Differentiate w.r.t. b

$$3$$

Steps Using Definition of a Derivative

Multiply \frac{24a^{4}}{b^{3}} times \frac{b^{4}}{8a^{4}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{24a^{4}b^{4}}{b^{3}\times 8a^{4}})$$

Cancel out 8b^{3}a^{4} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}b}(3b)$$

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

$$3b^{1-1}$$

Subtract 1 from 1.

$$3b^{0}$$

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

$$3\times 1$$

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

$$3$$