Solve a^2b^2c^6/abc^3

$$\frac { a ^ { 2 } b ^ { 2 } c ^ { 6 } } { a b c ^ { 3 } }$$

Differentiate w.r.t. a

$$bc^{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{b^{2}c^{6}}{bc^{3}}a^{2-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(bc^{3}a^{1})$$

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}.

$$bc^{3}a^{1-1}$$

Do the arithmetic.

$$bc^{3}a^{0}$$

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

$$bc^{3}\times 1$$

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

$$bc^{3}$$

Evaluate

$$abc^{3}$$

Solution Steps

Cancel out abc^{3} in both numerator and denominator.

$$abc^{3}$$