Question
Diffrentiate the following w.r.t.x
$\sqrt{e^{(3 x+2)}+5}$
$\sqrt{e^{(3 x+2)}+5}$
Differentiating w.r.t. x, we get
$\begin{aligned} \frac{d y}{d x} & =\frac{d}{d x}\left[e^{(3 x+2)}+5\right]^{\frac{1}{2}} \\ & =\frac{1}{2}\left[e^{(3 x+2)}+5\right]^{-\frac{1}{2}} \cdot \frac{d}{d x}\left[e^{(3 x+2)}+5\right] \\ & =\frac{1}{2 \sqrt{e^{(3 x+2)}+5}} \cdot\left[e^{(3 x+2)} \cdot \frac{d}{d x}(3 x+2)+0\right] \\ & =\frac{1}{2 \sqrt{e^{(3 x+2)}+5}} \cdot\left[e^{(3 x+2)} \cdot(3 \times 1+0)\right] \\ & =\frac{3 e^{(3 x+2)}}{2 \sqrt{e^{(3 x+2)}+5}} \cdot\end{aligned}$
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4x - 18 ≥ 0
$+x^2-2$. It is known that $a=-1$. Find the value of $b$.
$\int \frac{1}{2+\cos x-\sin x} \cdot d x$