Solve 3a^4b^9c^3/ab^8c

$$\frac { 3 a ^ { 4 } b ^ { 9 } c ^ { 3 } } { a b ^ { 8 } c }$$

Differentiate w.r.t. a

$$9b\left(ac\right)^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{3c^{3}b^{9}}{cb^{8}}a^{4-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(3bc^{2}a^{3})$$

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}.

$$3\times 3bc^{2}a^{3-1}$$

Do the arithmetic.

$$9bc^{2}a^{2}$$

Evaluate

$$3bc^{2}a^{3}$$

Solution Steps

Cancel out acb^{8} in both numerator and denominator.

$$3bc^{2}a^{3}$$