Solve 24/abc^2*a^2bc^2/12

$$\frac { 24 } { a b c ^ { 2 } } \times \frac { a ^ { 2 } b c ^ { 2 } } { 12 }$$

Evaluate

$$2a$$

Solution Steps

Multiply \frac{24}{abc^{2}} times \frac{a^{2}bc^{2}}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{24a^{2}bc^{2}}{abc^{2}\times 12}$$

Cancel out 12abc^{2} in both numerator and denominator.

$$2a$$

Differentiate w.r.t. a

$$2$$

Steps Using Definition of a Derivative

Multiply \frac{24}{abc^{2}} times \frac{a^{2}bc^{2}}{12} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{24a^{2}bc^{2}}{abc^{2}\times 12})$$

Cancel out 12abc^{2} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(2a)$$

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

$$2a^{1-1}$$

Subtract 1 from 1.

$$2a^{0}$$

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

$$2\times 1$$

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

$$2$$