find the derivative of sinX.cosX
Answers
Step-by-step explanation:
The product rule can be used to differentiate any function of the form
f
(
x
)
=
g
(
x
)
h
(
x
)
. It states that
f
'
(
x
)
=
g
'
(
x
)
h
(
x
)
+
g
(
x
)
h
'
(
x
)
.
The derivative of
sin
x
is
cos
x
and the derivative of
cos
x
is
−
sin
x
.
f
'
(
x
)
=
cos
x
(
cos
x
)
+
sin
x
(
−
sin
x
)
f
'
(
x
)
=
cos
2
x
−
sin
2
x
Use the identity
cos
2
x
=
cos
2
x
−
sin
2
x
:
f
'
(
x
)
=
cos
2
x
Answer:
● The product rule can be used to differentiate any function of the form
The product rule can be used to differentiate any function of the form f(x)=g(x)h(x). It states that f'(x)=g'(x)h(x)+g(x)h'(x).
The product rule can be used to differentiate any function of the form f(x)=g(x)h(x). It states that f'(x)=g'(x)h(x)+g(x)h'(x).The derivative of sinx is cox
The product rule can be used to differentiate any function of the form f(x)=g(x)h(x). It states that f'(x)=g'(x)h(x)+g(x)h'(x).The derivative of sinx is cox and the derivative of
The product rule can be used to differentiate any function of the form f(x)=g(x)h(x). It states that f'(x)=g'(x)h(x)+g(x)h'(x).The derivative of sinx is cox and the derivative of cosx is -sinx.f'(x)=cosx(cos+sinx(−sinx)f'(x)=cos2x−sin2x
+sinx(−sinx)f'(x)=cos2x−sin2xUse the identity
+sinx(−sinx)f'(x)=cos2x−sin2xUse the identity cos2x=cos2x−sin2x:f'(x)=cos2x
+sinx(−sinx)f'(x)=cos2x−sin2xUse the identity cos2x=cos2x−sin2x:f'(x)=cos2xHopefully this helps!