Solve 25xy^3/5xy^-1

$$\frac { 25 x y ^ { 3 } } { 5 x y ^ { - 1 } }$$

Evaluate

$$5y^{4}$$

Solution Steps

Cancel out 5x in both numerator and denominator.

$$\frac{5y^{3}}{\frac{1}{y}}$$

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

$$5y^{4}$$

Differentiate w.r.t. y

$$20y^{3}$$

Steps Using Definition of a Derivative

Cancel out 5x in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{5y^{3}}{\frac{1}{y}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(5y^{4})$$

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

$$4\times 5y^{4-1}$$

Multiply 4 times 5.

$$20y^{4-1}$$

Subtract 1 from 4.

$$20y^{3}$$