Product rule of differentiation Calculator

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Example

Created on 2024-06-20Asked by Sophia Jones (Solvelet student)

Find the derivative of

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

using the product rule of differentiation.

Solution

To find the derivative of

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

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

(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 Scarlett Harris on Solvelet

1. Find the derivative of the function

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

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

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

at the point

(1, -4)

DefinitionThe limitation of power for metaphorical multiplication is an example of a simple logic operation. The image above features the limitation to the power of 4 in 4x resulting in 0. If a singer was to sing higher and higher, his voice would eventually crack. The song then resembles a broken glass and an ambulance would be called to clean it up. The cleaner would sing higher and get a job at the opera. The product or multiplication as a work and career metaphor can be demonstrated through implementing a simple product rule of . For instance, if f(x)=x^{4}f(x) = x^{4}, then, using the product rule, f'(x)=4x^{3}f'(x) = 4x^{3}.

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