Find the derivative of the function y = (x2 + 7x) / (x+2) using the quotient rule.

Question

ScanSolve AI Tutor · Accepted Answer

To find dy/dx for the given function y = (x² + 7x)/(x+2), we will use the quotient rule. The quotient rule states that if y = u/v, then dy/dx = (v du/dx − u dv/dx)/(v²). Step 1: Identify u and v. Let u = x² + 7x; Let v = x+2 Step 2: Find the derivatives of u and v with respect to x. du/dx = d/dx(x² + 7x) = 2x + 7; dv/dx = d/dx(x+2) = 1 Step 3: Apply the quotient rule formula. dy/dx = ((x+2)(2x+7) − (x²+7x)(1))/((x+2)²) Step 4: Expand and simplify the numerator. Numerator = (x · 2x + x · 7 + 2 · 2x + 2 · 7) − (x² + 7x); Numerator = (2x² + 7x + 4x + 14) − (x² + 7x); Numerator = 2x² + 11x + 14 − x² − 7x; Numerator = (2x² − x²) + (11x − 7x) + 14; Numerator = x² + 4x + 14 Step 5: Write the final expression for dy/dx. dy/dx = (x² + 4x + 14)/((x+2)²)

Point	x	y
x-intercept	−7	0
x-intercept	0	0

Find the derivative of the function y = (x2 + 7x) / (x+2) using the quotient rule.

Answer

Step-by-step solution

Identify $u$ and $v$ .

Find the derivatives of $u$ and $v$ with respect to $x$ .

Apply the quotient rule formula.

Expand and simplify the numerator.

Write the final expression for $\frac{dy}{dx}$ .

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More Mathematics Questions

Find the derivative of the function y = (x2 + 7x) / (x+2) using the quotient rule.

Answer

Step-by-step solution

Identify uuu and vvv.

Find the derivatives of uuu and vvv with respect to xxx.

Apply the quotient rule formula.

Expand and simplify the numerator.

Write the final expression for dydx\frac{dy}{dx}dxdy​.

Still stuck on this one?

More Mathematics Questions

Identify $u$ and $v$ .

Find the derivatives of $u$ and $v$ with respect to $x$ .

Write the final expression for $\frac{dy}{dx}$ .