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Question

Find the equation of the tangent to the curve with equation
y=3cosh2xsinhx at the point x=ln2

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Solution

Slope of the curve at x=ln2 is y(ln2)

y(x)=6sinh2xcoshx

y(ln2)=6(eln2eln22)(eln2+eln22)

y(ln2)=6(2)0

y(ln2)=12

And y(ln2)=2

Equation of tangent =y(2)=12(xln2)

y=12x(2+12ln2) is the equation of the tangent

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