Solve a^3b/2asqrt{bc}

$$\frac { a ^ { 3 } b } { 2 a \sqrt { b c } }$$

Differentiate w.r.t. a

$$\frac{ab}{\sqrt{bc}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{b}{2\sqrt{bc}}a^{3-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{b}{2\sqrt{bc}}a^{2})$$

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}.

$$2\times \frac{b}{2\sqrt{bc}}a^{2-1}$$

Do the arithmetic.

$$\frac{b}{\sqrt{bc}}a^{1}$$

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

$$\frac{b}{\sqrt{bc}}a$$

Evaluate

$$\frac{ba^{2}}{2\sqrt{bc}}$$