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## Differential Calculus

### Course: Differential Calculus>Unit 3

Lesson 8: Differentiation using multiple rules

# Applying the chain rule and product rule

Example showing multiple strategies for taking a derivative that involves both the product rule and the chain rule.

## Want to join the conversation?

• After squaring (x^2*sin(x)), wouldn't you have to distribute the 3 before distributing into the other function?
• Distribute the 3 into what is then x^4sin^2(x)? if that is what you are referring to, you don't need to distribute since it's all multiplication.
• Isn't it would be much more simple if the derivative is taken w.r.t (x^2 sin x)?
• That's basically the chain rule. In the end you want the derivative with respect to x, which is why you use d/dx The chain rule is the outside function with respect to the inside function times the inside function with respect to x, ot the next inner function if it was more than just one function inside of another.
• how do you solve for dy/dx or is it the same??
• It's the same. In this video he uses (x^2sin(x))^3 to represent y. Since y is a function of x you can just replace y with its function form where it has x.

so if y=x^2 dy/dx can be rewritten as d(x^2)/dx or d/dx (x^2)
• what should i do in this case f(x)=sin3x^2(5x3-1)^1/3?