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Solve 8x3/2n – 8x-3/2n = 63.

Put \(\begin{array}{l} \mathrm{x}^{\frac{3}{2 \mathrm{n}}}=\mathrm{t},\\ 8 \mathrm{t}-\frac{8}{\mathrm{t}}=63\\ \Rightarrow 8 \mathrm{t}^{2}-8=63 \mathrm{t}\\ \Rightarrow 8 \mathrm{t}^{2}-63 \mathrm{t}-8=0\\ \Rightarrow 8 \mathrm{t}^{2}-64 \mathrm{t}+\mathrm{t}-8=0\\ \Rightarrow 8... View Article

Differentiate esinx.

Given \(\begin{array}{l}\mathbf{y}=\mathbf{e}^{\sin \mathrm{x}}\\ \text { By using chain rule, }\\ \frac{\mathrm{d} y}{\mathrm{dx}}=\mathrm{e}^{\sin \mathrm{x}} \frac{\mathbf{d} \sin \mathrm{x}}{\mathrm{dx}}\\ \frac{\mathrm{dy}}{\mathrm{dx}}=\mathrm{e}^{\sin \mathrm{x}} \cos \mathrm{x}\end{array}... View Article