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Question Number 203448 by hardmath last updated on 19/Jan/24

$$\mathrm{y}=\sin 3\mathrm{x}-\ln (3\mathrm{x}+1)+3^{2\mathbf{x}}$$$$\mathrm{find}:{\mathrm{y}}^{{}^{\prime }}=?$$

Commented by hardmath last updated on 19/Jan/24

$$$$find the derivative of the function

Answered by mr W last updated on 19/Jan/24

$$y^{\prime }=3\cos 3x-\frac{3}{3x+1}+3^{2x}\times 2\ln 3$$

Commented by hardmath last updated on 19/Jan/24

$$\mathrm{thank}\mathrm{you}\mathrm{dear}\mathrm{professor}$$

Answered by MrGHK last updated on 19/Jan/24

$${\mathbf{y}}^{{}^{\prime }}=\frac{\mathbf{d}}{\mathbf{dx}}\left(3\mathbf{x}\right).\frac{\mathbf{d}}{\mathbf{du}}\left(\mathbf{sin}\left(\mathbf{u}\right)\right)-\frac{\mathbf{d}}{\mathbf{dx}}(3\mathbf{x}+1).\frac{\mathbf{d}}{\mathbf{du}}\left(\mathbf{ln}\left(\mathbf{u}\right)\right)+\frac{\mathbf{d}}{\mathbf{dx}}\left(2\mathbf{xln}\left(3\right)\right).\frac{\mathbf{d}}{\mathbf{du}}{\mathbf{e}}^{\mathbf{u}}$$$${\mathbf{y}}^{{}^{\prime }}=3\mathbf{cos}\left(3\mathbf{x}\right)-\frac{3}{3\mathbf{x}+1}+2\mathbf{ln}\left(3\right)3^{2\mathbf{x}}$$

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