Find $\frac{d y}{d x}$
$y = \cot x - 6 \sqrt{x} + \frac{8}{e^{x}}$

Answer

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Answer

Thus, the derivative of the given function is $- \csc^{2} x - 3 x^{- \frac{1}{2}} - \frac{8}{e^{x}}$ .

Steps

Step 1 ：First, we need to find the derivative of each term in the equation separately.

Step 2 ：For the first term, $y = \cot x$ , the derivative is $- \csc^{2} x$ .

Step 3 ：For the second term, $y = - 6 \sqrt{x}$ , the derivative is $- 3 x^{- \frac{1}{2}}$ .

Step 4 ：For the third term, $y = \frac{8}{e^{x}}$ , the derivative is $- \frac{8}{e^{x}}$ .

Step 5 ：Adding these derivatives together, we get $\frac{d y}{d x} = - \csc^{2} x - 3 x^{- \frac{1}{2}} - \frac{8}{e^{x}}$ .

Step 6 ：Thus, the derivative of the given function is $- \csc^{2} x - 3 x^{- \frac{1}{2}} - \frac{8}{e^{x}}$ .