How to solve (y)/(-(y)^(2))

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve (y)/(-(y)^(2)) | Equatix

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Question

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

Evaluate

$-\frac{1}{y}$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(y^{1}\right)^{1}\times \frac{1}{-y^{2}}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$1^{1}\left(y^{1}\right)^{1}\left(-1\right)\times \frac{1}{y^{2}}$$

Use the Commutative Property of Multiplication.

$$1^{1}\left(-1\right)\left(y^{1}\right)^{1}\times \frac{1}{y^{2}}$$

To raise a power to another power, multiply the exponents.

$$1^{1}\left(-1\right)y^{1}y^{2\left(-1\right)}$$

Multiply $2$ times $-1$.

$$1^{1}\left(-1\right)y^{1}y^{-2}$$

To multiply powers of the same base, add their exponents.

$$1^{1}\left(-1\right)y^{1-2}$$

Add the exponents $1$ and $-2$.

$$1^{1}\left(-1\right)\times \frac{1}{y}$$

Raise $-1$ to the power $-1$.

$$-\frac{1}{y}$$

Show Solution

Differentiate w.r.t. y

$\frac{1}{y^{2}}$

Solution Steps

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

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}y}(-\frac{1}{y})$$

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 $nax^{n-1}$.

$$-\left(-1\right)y^{-1-1}$$