Question

If $y(x) = (f \circ g)(x)$, then $y'(x)$ can be denoted: (choose all correct answers) $f'(g)g'(x)$ $f'(x)g'(x)$ $\frac{df}{dg}\frac{dg}{dx}$ $f'(g)g(x)$

          If $y(x) = (f \circ g)(x)$, then $y'(x)$ can be denoted: 
(choose all correct answers)
$f'(g)g'(x)$
$f'(x)g'(x)$
$\frac{df}{dg}\frac{dg}{dx}$
$f'(g)g(x)$

If y(x) = (f ∘ g)(x), then y'(x) can be denoted:
(choose all correct answers)
f'(g)g'(x)
f'(x)g'(x)
(df)/(dg)(dg)/(dx)
f'(g)g(x)

Added by Martin G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

01/03/2023

Step 1

This is because the derivative of a composition of functions is the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function. Show more…

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If y(x) = (f @ g)(x), then y'(x) can be denoted: (choose all correct answers) f'(g) * g'(x) f'(x) * g'(x) (df)/(dg) * (dg)/(dx) f'(g') * g(x) If y - f o g, then y can be denoted: (choose all correct answers f'g)gx) f(x)gx) df dg dg dx f'(g)g(x)