Question

Find the dy/dx, ify=sinx/cosx

sec^2x
sec2x
cosecx
coshx

Answer 1

Answer on Question #47034 - Math - Differential Calculus | Equations

Find the dy/dx, if $y = \sin x / \cos x$

sec^2x

sec^2x

cosecx

coshx

Solution:

We have if

$$y = \frac {\sin x}{\cos x} = \tan x$$

then

$$\frac {d y}{d x} = \frac {1}{(\cos x) ^ {2}}$$

Hence

$$\frac {d y}{d x} = \frac {1}{(\cos x) ^ {2}} = (\sec x) ^ {2}$$

because

$$\frac {1}{\cos x} = \sec x$$

Answer: $\frac{dy}{dx} = (\sec x)^2$

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