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Popular >

d/(dv)(ln(cosh(2v))-1/2 tanh^2(2v))

Solution

\frac{d}{d v} (ln (cosh (2 v)) - \frac{1}{2} tanh^{2} (2 v))

Solution

2 tanh^{3} (2 v)

Solution steps

\frac{d}{d v} (ln (cosh (2 v)) - \frac{1}{2} tanh^{2} (2 v))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d v} (ln (cosh (2 v))) - \frac{d}{d v} (\frac{1}{2} tanh^{2} (2 v))

\frac{d}{d v} (ln (cosh (2 v))) = 2 tanh (2 v)

\frac{d}{d v} (\frac{1}{2} tanh^{2} (2 v)) = 2 sech^{2} (2 v) tanh (2 v)

= 2 tanh (2 v) - 2 sech^{2} (2 v) tanh (2 v)

Simplify

2 tanh (2 v) - 2 sech^{2} (2 v) tanh (2 v) : 2 tanh^{3} (2 v)

= 2 tanh^{3} (2 v)

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Frequently Asked Questions (FAQ)

What is the d/(dv)(ln(cosh(2v))-1/2 tanh^2(2v)) ?
The d/(dv)(ln(cosh(2v))-1/2 tanh^2(2v)) is 2tanh^3(2v)
What is the first d/(dv)(ln(cosh(2v))-1/2 tanh^2(2v)) ?
The first d/(dv)(ln(cosh(2v))-1/2 tanh^2(2v)) is 2tanh^3(2v)