Product Rule Calculator

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Example

Created on 2024-06-20Asked by Amelia Martinez (Solvelet student)

Find the derivative of

f(x) = (x^2 + 3x)(2x - 1)

using the product rule.

Solution

To find the derivative of

f(x) = (x^2 + 3x)(2x - 1)

using the product rule: 1. Apply the product rule for differentiation:

(uv)' = u'v + uv'.

2. Identify

u

and

v

u = x^2 + 3x, \quad v = 2x - 1.

3. Compute the derivatives of

u

and

v

u' = 2x + 3, \quad v' = 2.

4. Apply the product rule:

\begin{aligned} f'(x) &= (2x + 3)(2x - 1) + (x^2 + 3x)(2) \\ &= 4x^2 - 2x + 6x - 3 + 2x^2 + 6x \\ &= 6x^2 + 10x - 3. \end{aligned}

Therefore, the derivative of

f(x)

f'(x) = 6x^2 + 10x - 3

. Solved on Solvelet with Basic AI Model

Some of the related questions asked by Lucas Anderson on Solvelet

1. Find the derivative of the function

f(x) = (x^2 + 1)(3x - 2)

.2. Calculate the slope of the tangent line to the curve

y = (2x + 1)(x - 3)

at the point

(2, -5)

DefinitionProduct rule says a rule to compute the derivative of the product of two functions. When u(x) and v(x) are functions of x→(uv)′=u′v+uv′. To take an example: If u(x)=x2 and v(x)=sin(x), then (uv)′=2xsin(x)+x2cos(x).

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