Solve 12a^10/6a^6*2a=

$$\frac { 12 a ^ { 10 } } { 6 a ^ { 6 } \cdot 2 a } =$$

Evaluate

$$a^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$\frac{12a^{10}}{6a^{7}\times 2}$$

Cancel out 2\times 6a^{7} in both numerator and denominator.

$$a^{3}$$

Differentiate w.r.t. a

$$3a^{2}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{12}{12a}a^{10-6})$$

Do the arithmetic.

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

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}.

$$4\times \frac{1}{a}a^{4-1}$$

Do the arithmetic.

$$\frac{4}{a}a^{3}$$