Solve 9x^16/6(x^2)^3x^2

$$\frac { 9 x ^ { 16 } } { 6 ( x ^ { 2 } ) ^ { 3 } x ^ { 2 } }$$

Evaluate

$$\frac{3x^{8}}{2}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{9x^{16}}{6x^{6}x^{2}}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$\frac{9x^{16}}{6x^{8}}$$

Cancel out 3x^{8} in both numerator and denominator.

$$\frac{3x^{8}}{2}$$

Differentiate w.r.t. x

$$12x^{7}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{9}{6x^{6}}x^{16-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3}{2x^{6}}x^{14})$$

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}.

$$14\times \frac{3}{2x^{6}}x^{14-1}$$

Do the arithmetic.

$$\frac{21}{x^{6}}x^{13}$$