# Calculus chain rule questions

#### KK88

Hi I have a few calculus questions, could you please explain how to get the final answer too, thanks.

Derivative of :   dy/dx here dy/dx here dy/dt here

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#### dwsmith

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Hi I have a few calculus questions, could you please explain how to get the final answer too, thanks.

Derivative of : Chain rule of the chain rule with a product rule chain rule dy/dx here
chain rule dy/dx here
product rule with chain dy/dt here
chain

You haven't attempted much so start by trying that.

#### KK88

Ok I figured out the middle three but I cannot quite get the first one and last one

#### dwsmith

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$$\displaystyle (cos\big(e^{x^2cos(x)}\big))^{\frac{1}{2}}$$

$$\displaystyle \frac{1}{2}(cos\big(e^{x^2cos(x)}\big))^{\frac{-1}{2}}(-sin\big(e^{x^2cos(x)}\big))(e^{x^2cos(x)}(2xcos(x)-x^2sin(x)))$$

I am not going to simplify that.

• KK88

#### dwsmith

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$$\displaystyle e^{2sin(8t)}$$

$$\displaystyle 8e^{2sin(8t)}2cos(8t)=16e^{2sin(8t)}cos(8t)$$

• KK88

#### KK88

Thanks for the responses.
The second one is correct however I still cant get the first one right, I input this: • Rapha

#### dwsmith

MHF Hall of Honor
The first one is correct too. Here is the maple output.

• KK88

#### dwsmith

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$$\displaystyle \frac{1}{2}(cos\big(e^{x^2cos(x)}\big))^{\frac{-1}{2}}(-sin\big(e^{x^2cos(x)}\big))(e^{x^2cos(x)}(2xcos(x)-x^2sin(x)))$$

You need to have this quantity in parenthesis.
(2xcos(x)-x^2sin(x))

• KK88

#### KK88

Thanks that did it.