Question #180580

find dy/dx

y = 3cosh √x -3e^2x


1
Expert's answer
2021-04-15T07:33:20-0400
y=3coshx3e2xddx[y]=ddx[3cosh(x)3e2x]=3ddx[cosh(x)]3e2ddx[x]=3sinh(x)ddx[x]3e21=3sinh(x)12x1213e2    dydx=3sinh(x)2x3e2y=3cosh \sqrt x -3e^2x\\ \frac{\mathrm{d}}{\mathrm{d}x}[y]=\frac{\mathrm{d}}{\mathrm{d}x}\left[3\cosh\left(\sqrt{x}\right)-3\mathrm{e}^2x\right]\\ \qquad \qquad \quad =3\cdot \tfrac{\mathrm{d}}{\mathrm{dx}}[\cosh(\sqrt{x})]-3\mathrm{e}^2 \cdot \tfrac{\mathrm{d}}{\mathrm{dx}}[x]\\ \qquad \qquad \quad =3\sinh(\sqrt x) \cdot \frac{\mathrm{d}}{\mathrm{dx}}[\sqrt x]-3\mathrm{e}^2 \cdot 1\\ \qquad \quad= 3\sinh(\sqrt x) \cdot \tfrac{1}{2}x^{\tfrac{1}{2}-1}-3\mathrm{e}^2\\ \implies \frac{\mathrm{dy}}{\mathrm{dx}}= \frac{3 \sinh(\sqrt x)}{2\sqrt x}-3\mathrm{e}^2


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