How to solve y/(3y + 6)

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/(3y + 6) | Equatix

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

Question

$$\frac{y}{3y+6}$$

Differentiate w.r.t. y

$\frac{2}{3\left(y+2\right)^{2}}$

Steps Using Derivative Rule for Quotient

For any two differentiable functions, the derivative of the quotient of two functions is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the denominator squared.

$$\frac{\left(3y^{1}+6\right)\frac{\mathrm{d}}{\mathrm{d}y}(y^{1})-y^{1}\frac{\mathrm{d}}{\mathrm{d}y}(3y^{1}+6)}{\left(3y^{1}+6\right)^{2}}$$

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 $nax^{n-1}$.

$$\frac{\left(3y^{1}+6\right)y^{1-1}-y^{1}\times 3y^{1-1}}{\left(3y^{1}+6\right)^{2}}$$

Do the arithmetic.

$$\frac{\left(3y^{1}+6\right)y^{0}-y^{1}\times 3y^{0}}{\left(3y^{1}+6\right)^{2}}$$

Expand using distributive property.

$$\frac{3y^{1}y^{0}+6y^{0}-y^{1}\times 3y^{0}}{\left(3y^{1}+6\right)^{2}}$$

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

$$\frac{3y^{1}+6y^{0}-3y^{1}}{\left(3y^{1}+6\right)^{2}}$$

Combine like terms.

$$\frac{\left(3-3\right)y^{1}+6y^{0}}{\left(3y^{1}+6\right)^{2}}$$

Subtract $3$ from $3$.

$$\frac{6y^{0}}{\left(3y^{1}+6\right)^{2}}$$

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

$$\frac{6y^{0}}{\left(3y+6\right)^{2}}$$

For any term $t$ except $0$, $t^{0}=1$.

$$\frac{6\times 1}{\left(3y+6\right)^{2}}$$

For any term $t$, $t\times 1=t$ and $1t=t$.

$$\frac{6}{\left(3y+6\right)^{2}}$$

Show Solution

Evaluate

$\frac{y}{3\left(y+2\right)}$