Question

If y=5e^x/cosx,differentiate with respect to x.

A. 5e^x(cosx+sinx)/cos^2x

B. e^x(cosx+sinx)/cos^2x

C. 5e^x(cosx+sinx)/cos^3x

D. 5e(cosx+sinx)/cos^2x

Answer 1

Answer on Question #47073 – Math – Differential Calculus – Equations

Question.

If $y = \frac{5e^x}{\cos x}$ differentiate with respect to $x$.

A. $\frac{5e^x(\cos x + \sin x)}{(\cos x)^2}$

B. $\frac{e^x(\cos x + \sin x)}{(\cos x)^2}$

C. $\frac{5e^x(\cos x + \sin x)}{(\cos x)^3}$

D. $\frac{5e(\cos x + \sin x)}{(\cos x)^2}$

Solution.

$$y' = \frac{(5e^x)/\cos x - 5e^x(\cos x)}{(\cos x)^2} = \frac{5e^x \cos x + 5e^x \sin x}{(\cos x)^2} = \frac{5e^x (\cos x + \sin x)}{(\cos x)^2}.$$

We applied differentiation rule for quotient.

Answer.

A. $\frac{5e^x(\cos x + \sin x)}{(\cos x)^2}$

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