Solve y^10y^0/y^7

$$\frac{ { y }^{ 10 } { y }^{ 0 } }{ { y }^{ 7 } }$$

Evaluate

$$y^{3}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 10 and 0 to get 10.

$$\frac{y^{10}}{y^{7}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 7 from 10 to get 3.

$$y^{3}$$

Differentiate w.r.t. y

$$3y^{2}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 10 and 0 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{y^{10}}{y^{7}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 7 from 10 to get 3.

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

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

$$3y^{3-1}$$

Subtract 1 from 3.

$$3y^{2}$$