Solve 8a^2bc/2ac=

$$\frac { 8 a ^ { 2 } b c } { 2 a c } =$$

Differentiate w.r.t. a

$$4b$$

Solution Steps

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

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

Do the arithmetic.

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

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}.

$$4ba^{1-1}$$

Do the arithmetic.

$$4ba^{0}$$

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

$$4b\times 1$$

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

$$4b$$

Evaluate

$$4ab$$

Solution Steps

Cancel out 2ac in both numerator and denominator.

$$4ab$$