Answer to Question #180580 in Calculus for maya

Question

find dy/dx

y = 3cosh √x -3e^2x

Answer 1

$$y=3cosh \sqrt x -3e^2x\\ \frac{\mathrm{d}}{\mathrm{d}x}[y]=\frac{\mathrm{d}}{\mathrm{d}x}\left[3\cosh\left(\sqrt{x}\right)-3\mathrm{e}^2x\right]\\ \qquad \qquad \quad =3\cdot \tfrac{\mathrm{d}}{\mathrm{dx}}[\cosh(\sqrt{x})]-3\mathrm{e}^2 \cdot \tfrac{\mathrm{d}}{\mathrm{dx}}[x]\\ \qquad \qquad \quad =3\sinh(\sqrt x) \cdot \frac{\mathrm{d}}{\mathrm{dx}}[\sqrt x]-3\mathrm{e}^2 \cdot 1\\ \qquad \quad= 3\sinh(\sqrt x) \cdot \tfrac{1}{2}x^{\tfrac{1}{2}-1}-3\mathrm{e}^2\\ \implies \frac{\mathrm{dy}}{\mathrm{dx}}= \frac{3 \sinh(\sqrt x)}{2\sqrt x}-3\mathrm{e}^2$$