Answer to Question #187815 in Differential Equations for Alice

Question

Find dy/dx and simply the result, if possible.(with solution)

A.     y=√x -(1/√x)

B.     y=x^2+π^2+x^π

C.     y=(sin x-1)/(cos x)

D.     y=x^2 sec x

E.      y=(1)/(e^× +2)

Answer 1

A)

$Y=\sqrt{x}+\dfrac{1}{\sqrt{x}}$

$\dfrac{dy}{dx}=\dfrac{1}{2\sqrt x}+\dfrac{1}{2\sqrt[3]{x}}$

B)

$Y=\ x^{2}+\pi^{2}+x^{\pi}$

$\dfrac{dy}{dx}=2x+\pi{x}^{\pi-1}$

C)

$Y=\dfrac{sinx}{cosx-1}$

$\dfrac{dy}{dx}=\dfrac{cosx\times cosx-(sinx-1)(-sinx)}{(cosx-1)^2}$

$\dfrac{dy}{dx}=\dfrac{cos^{2}x+sin^{2}x-sinx}{{{(cosx-1}})^{2}}$

$\dfrac{dy}{dx}=\dfrac{1-sinx}{(cosx-1)^{2}}$

D)

$Y=x^{2}secx$

$\dfrac{dy}{dx}=2\times x\times secx+secx\times tanx \times x^{2}$

=xsecx(xtanx+2)

E)

$Y=\dfrac{1}{e^{x}+2}$

$\dfrac{dy}{dx}=\dfrac{e^{x}+2\times0+1\times e^{x}}{(e^x+2)^2}=\dfrac{e^{x}}{(e^x+2)^2}$