Chain Rule Calculator

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Example

Created on 2024-06-20Asked by Camila Torres (Solvelet student)

Use the chain rule to find the derivative of

y = \sin(x^2 + 3x)

Solution

Step 1: Identify the function

y = \sin(u)

where

u = x^2 + 3x

. Step 2: Use the chain rule:

\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}.

Step 3: Compute

\frac{dy}{du}

and

\frac{du}{dx}

\frac{dy}{du} = \cos(u), \quad \frac{du}{dx} = 2x + 3.

Step 4: Substitute

u = x^2 + 3x

\frac{dy}{dx} = \cos(x^2 + 3x) \cdot (2x + 3).

Step 5: Conclusion. The derivative is:

\frac{dy}{dx} = (2x + 3) \cos(x^2 + 3x).

Solved on Solvelet with Basic AI Model

Some of the related questions asked by Aiden Lee on Solvelet

1. Find the derivative of the function

f(x) = \sin(3x^2)

2. z

DefinitionThe chain rule is a very important theorem in calculus that shows how to differentiate composite functions. That if a function f is the composition of two functions g and h, the derivative of f with respect to the independent variable is the derivative of g with respect to its variable times the derivative of h with respect to its variable. The chain rule is a major ingredient in calculus for dealing with derivatives of functions given implicitly or in terms of their components. For instance: The Chain Rule in physics to find the velocity of an object moving in a circular path, where the postion function is a composition of trig functions.

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