Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
If
y
=
f
(
g
(
x
)
)
y=f(g(x))
y
=
f
(
g
(
x
))
where both
f
f
f
and
g
g
g
are differentiable, which of the following expressions correctly gives
d
y
d
x
\dfrac{dy}{dx}
d
x
d
y
in terms of
f
f
f
and
g
g
g
? a)
f
′
(
x
)
g
′
(
x
)
f'(x)\,g'(x)
f
′
(
x
)
g
′
(
x
)
b)
f
′
(
g
(
x
)
)
g
′
(
x
)
f'(g(x))\,g'(x)
f
′
(
g
(
x
))
g
′
(
x
)
c)
f
′
(
g
(
x
)
)
+
g
′
(
x
)
f'(g(x))+g'(x)
f
′
(
g
(
x
))
+
g
′
(
x
)
d)
g
′
(
f
(
x
)
)
f
′
(
x
)
g'(f(x))\,f'(x)
g
′
(
f
(
x
))
f
′
(
x
)
Browse the problem library