Solve 15x^6y^-9/5xy^-11

$$\frac { 15 x ^ { 6 } y ^ { - 9 } } { 5 x y ^ { - 11 } }$$

Evaluate

$$3y^{2}x^{5}$$

Solution Steps

Cancel out 5x in both numerator and denominator.

$$\frac{3y^{-9}x^{5}}{y^{-11}}$$

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

$$3y^{2}x^{5}$$

Differentiate w.r.t. x

$$15y^{2}x^{4}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{15}{y^{9}\times \frac{5}{y^{11}}}x^{6-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3y^{2}x^{5})$$

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}.

$$5\times 3y^{2}x^{5-1}$$

Do the arithmetic.

$$15y^{2}x^{4}$$