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Question Number 158049 by zainaltanjung last updated on 30/Oct/21

$$\mathrm{Find}\mathrm{derivative}\mathrm{of}\mathrm{this}\mathrm{function}$$$$1).\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}.\sin \mathrm{x}$$$$2).\mathrm{f}\left(\mathrm{x}\right)={\mathrm{e}}^{5\mathrm{x}}.\log {}_2\left(3\mathrm{x}\right)$$$$3).\mathrm{f}\left(\mathrm{x}\right)=3^{3\mathrm{x}}.(2\mathrm{x}-1)$$$$4).\mathrm{f}\left(\mathrm{x}\right)=\frac{{3\mathrm{x}}^2-2}{4\mathrm{x}+1}$$

Answered by MathsFan last updated on 30/Oct/21

$$1.{\mathrm{f}}^{\prime }\left(\mathrm{x}\right)=\mathrm{x}\bullet \frac{\mathrm{dy}}{\mathrm{dx}}\mathrm{sinx}+\mathrm{sinx}\frac{\mathrm{dy}}{\mathrm{dx}}\mathrm{x}$$$${\mathrm{f}}^{\prime }\left(\mathrm{x}\right)=\mathrm{xcosx}+\mathrm{sinx}$$

Answered by MathsFan last updated on 30/Oct/21

$$4.{\mathrm{f}}^{\prime }\left(\mathrm{x}\right)=\frac{(4\mathrm{x}+1)\left(6\mathrm{x}\right)-({3\mathrm{x}}^2-2)\left(4\right)}{{(4\mathrm{x}+1)}^2}$$$${\mathrm{f}}^{\prime }\left(\mathrm{x}\right)=\frac{6\mathrm{x}-{6\mathrm{x}}^2+8}{{(4\mathrm{x}+1)}^2}$$

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