Solve 12a^3*5a^4/5a*6a^2

$$\frac { 12 a ^ { 3 } \times 5 a ^ { 4 } } { 5 a \times 6 a ^ { 2 } }$$

Evaluate

$$2a^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{12a^{7}\times 5}{5a\times 6a^{2}}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{12a^{7}\times 5}{5a^{3}\times 6}$$

Cancel out 5\times 6a^{3} in both numerator and denominator.

$$2a^{4}$$

Differentiate w.r.t. a

$$8a^{3}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{60a^{4}}{30a^{2}}a^{3-1})$$

Do the arithmetic.

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

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}.

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

Do the arithmetic.

$$4a^{2}a^{1}$$

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

$$4a^{2}a$$