Solve 8ab^2c/24a^2bc^3

$$\frac { 8 a b ^ { 2 } c } { 24 a ^ { 2 } b c ^ { 3 } }$$

Differentiate w.r.t. a

$$-\frac{b}{3\left(ac\right)^{2}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{8cb^{2}}{24bc^{3}}a^{1-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{b}{3c^{2}}\times \frac{1}{a})$$

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}.

$$-\frac{b}{3c^{2}}a^{-1-1}$$

Do the arithmetic.

$$\left(-\frac{b}{3c^{2}}\right)a^{-2}$$

Evaluate

$$\frac{b}{3ac^{2}}$$

Solution Steps

Cancel out 8abc in both numerator and denominator.

$$\frac{b}{3ac^{2}}$$