Solve x^-5y^4y^7/x^-5

$$\frac { x ^ { - 5 } y ^ { 4 } y ^ { 7 } } { x ^ { - 5 } }$$

Evaluate

$$y^{11}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 7 to get 11.

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

Cancel out x^{-5} in both numerator and denominator.

$$y^{11}$$

Differentiate w.r.t. y

$$11y^{10}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 7 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{x^{-5}y^{11}}{x^{-5}})$$

Cancel out x^{-5} in both numerator and denominator.

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

The derivative of ax^{n} is nax^{n-1}.

$$11y^{11-1}$$

Subtract 1 from 11.

$$11y^{10}$$