Hyperbolic Functions and Tangent Line Slope 2 at y=sinhx

[nameVoid]

Find the points on the graph of y=sinhx at which the tangent line has slope 2

dy/dx=coshx=2

(e^x+e^(-x))=4
x-x=ln4

 

[Gib Z]

You have used an incorrect property of logarithms.

$$\log (a+b) \neq \log a + \log b$$.

There is no "useful" property for the log of a sum.

For solve that equation you have, try thinking about how you can make that a quadratic equation in e^x.

 

[nameVoid]

y=sinhx
y'=coshx=2
cosh^2x-sinh^2x=1
sinh^2=3
sinhx=+||-3^(1/2)=(e^x-e^(-x))/2
e^x-e^(-x)=+||-2*3^(1/2)
x=ln(+||-2*3^(1/2))/2
y=+||-e^(1/2)

 

[nameVoid]

$$\frac{d}{dx}sinhx=coshx=2$$
$$cosh^2x-sinh^2x=1=4-sinh^2x$$
$$sinhx=3^{1/2}$$
$$sinhx=-3^{1/2}$$
$$sinhx=\frac{e^x-e^{-x}}{2}=3^{1/2}$$
$$e^x-e^{-x}=2*3^{1/2}$$
$$2x=ln2+ln(3^{1/2})$$
$$x=\frac{ln2+ln(3^{1/2})}{2}$$
using the same methods for sinhx=-3^(1/2) does not work since taking the natural log of -sqrt3 this probelms should be solvable without inverses