differentiate the following.
cot x -3 sin x +2 cosec x
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Answer:
-cosec²x-3cosx-2cosecxcotx is right answer
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Answer:
Derivative of sin hyperbolic functions:
\frac d{dx}\left(\sin hx\right)=\cos hx
dx
d
(sinhx)=coshx
\sin hx=\left(\frac{e^x-e^{-x}}2\right)sinhx=(
2
e
x
−e
−x
)
differentiating w.r.t x
\frac d{dx}\sin hx=\frac d{dx}\left(\frac{e^x-e^{-x}}2\right)
dx
d
sinhx=
dx
d
(
2
e
x
−e
−x
)
\frac d{dx}\sin hx=\frac12\frac d{dx}\left(e^x-e^{-x}\right)
dx
d
sinhx=
2
1
dx
d
(e
x
−e
−x
)
Now by using sum and difference rule.
\frac d{dx}\sin hx=\frac12\left[\frac d{dx}e^x-\frac d{dx}e^{-x}\right]
dx
d
sinhx=
2
1
[
dx
d
e
x
−
dx
d
e
−x
]
\frac d{dx}\sin hx=\frac12\left[e^x-e^{-x}\left(-1\right)\right]
dx
d
sinhx=
2
1
[e
x
−e
−x
(−1)]
\frac d{dx}\sin hx=\frac12\left(e^x+e^{-x}\right)
dx
d
sinhx=
2
1
(e
x
+e
−x
)
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