Solve 3x^14y^11/18x^2

$$\frac { 3 x ^ { 14 } y ^ { 11 } } { 18 x ^ { 2 } }$$

Differentiate w.r.t. x

$$2\left(xy\right)^{11}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3y^{11}}{18}x^{14-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{y^{11}}{6}x^{12})$$

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}.

$$12\times \frac{y^{11}}{6}x^{12-1}$$

Do the arithmetic.

$$2y^{11}x^{11}$$

Evaluate

$$\frac{y^{11}x^{12}}{6}$$

Solution Steps

Cancel out 3x^{2} in both numerator and denominator.

$$\frac{y^{11}x^{12}}{6}$$