Solve 30a^3b^2/24a^2b^2c

$$\frac { 30 a ^ { 3 } b ^ { 2 } } { 24 a ^ { 2 } b ^ { 2 } c }$$

Differentiate w.r.t. a

$$\frac{5}{4c}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{30b^{2}}{24cb^{2}}a^{3-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{5}{4c}a^{1})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$\frac{5}{4c}a^{1-1}$$

Do the arithmetic.

$$\frac{5}{4c}a^{0}$$

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

$$\frac{5}{4c}\times 1$$

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

$$\frac{5}{4c}$$

Evaluate

$$\frac{5a}{4c}$$

Solution Steps

Cancel out 6a^{2}b^{2} in both numerator and denominator.

$$\frac{5a}{4c}$$