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Q. 3

Expert-verifiedFound in: Page 209

Book edition
1st

Author(s)
Peter Kohn, Laura Taalman

Pages
1155 pages

ISBN
9781429241861

State the chain rule for differentiating a composition $g\left(h\right(x\left)\right)$ of two functions expressed

(a) in “prime” notation and

(b) in Leibniz notation.

a) In prime notation the derivative is $\left(g\circ h\right)\text{'}\left(x\right)=g\text{'}\left(h\right(x\left)\right)\times h\text{'}\left(x\right)$

b) In Leibniz notation the derivative is:$\frac{dg}{dx}=\frac{dg}{dh}\times \frac{dh}{dx}$

The composite function is:

$g\left(h\right(x\left)\right)$

In prime notation the derivative of the function is written as:

$(g\circ h)\text{'}\left(x\right)=g\text{'}\left(h\right(x\left)\right)\times h\text{'}\left(x\right)$

In Leibniz notation, the derivative is:

$\frac{dg}{dx}=\frac{dg}{dh}\times \frac{dh}{dx}$

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