Solve y^2y^4/yy^3

$$\frac { y ^ { 2 } y ^ { 4 } } { y y ^ { 3 } }$$

Evaluate

$$y^{2}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\frac{y^{6}}{yy^{3}}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{y^{6}}{y^{4}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 6 to get 2.

$$y^{2}$$

Differentiate w.r.t. y

$$2y$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{y^{6}}{yy^{3}})$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{y^{6}}{y^{4}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 6 to get 2.

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

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

$$2y^{2-1}$$

Subtract 1 from 2.

$$2y^{1}$$

For any term t, t^{1}=t.

$$2y$$