Solve y^4*y/y^-2

$$\frac{ { y }^{ 4 } \times y }{ { y }^{ -2 } }$$

Evaluate

$$y^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{y^{5}}{y^{-2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -2 from 5 to get 7.

$$y^{7}$$

Differentiate w.r.t. y

$$7y^{6}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{y}{1}y^{4-\left(-2\right)})$$

Do the arithmetic.

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

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}.

$$6yy^{6-1}$$

Do the arithmetic.

$$6yy^{5}$$