- #1

Nate Learning

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- 0

Should I start off by squaring both sides to get rid of the radical on the left? and then start the derivative process? Thank you.

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- MHB
- Thread starter Nate Learning
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- #1

Nate Learning

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- 0

Should I start off by squaring both sides to get rid of the radical on the left? and then start the derivative process? Thank you.

- #2

skeeter

- 1,104

- 1

Looking at the square of the right side, i probably would not.

- #3

Opalg

Gold Member

MHB

- 2,779

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You certainly could do it that way, but I don't see that it would be any easier than just differentiating the equation as it stands. Write it as $$\bigl(3x^7 + y^2\bigr)^{1/2} = \sin^2y + 100xy,$$ and differentiate both sides with respect to $x$ using the chain rule.View attachment 11217

Should I start off by squaring both sides to get rid of the radical on the left? and then start the derivative process? Thank you.

- #4

jonah1

- 108

- 0

From which book did you get this challenging derivative?View attachment 11217

Should I start off by squaring both sides to get rid of the radical on the left? and then start the derivative process? Thank you.

- #5

HOI

- 923

- 2

The derivative of $3x^7+ y^2$ with respect to x is $21x^6+ 2y\frac{dy}{dx}$ so the derivative of $(3x^7+ y^2)^{1/2}$ is $\frac{1}{2}(3x^7+ y^2)^{-1/2}(21x^6+ 2y\frac{dy}{dx})$.

The derivative of $sin^2(y)$ with respect to x is $2 sin(y) cos(y)\frac{dy}{dx}$.

And the derivative of $100 xy$ with respect to x is $100y+ 100x\frac{dy}{dx}$.

So the derivative of $(3x^7+y^2)^{1/2}= sin^2(y)+ 100xy$ with respect to x is $\frac{1}{2}(3x^7+ y^2)^{-1/2}(21x^6+ 2y\frac{dy}{dx})= 2 sin(y) cos(y)\frac{dy}{dx}+ 100y+ 100x\frac{dy}{dx}$.

Solve that equation for $\frac{dy}{dx}$.

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