$\"\"$

The function is $\"f\\left$ .

Differentiate on each side with respect to $\"x\"$ .

$\"f\'\\left$ .

Product rule of derivatives: $\"(uv)\'=uv\'+vu\'\"$ .

$\"\\\\f\'\\left$

$\"\\\\f\'\'\\left$

$\"\\\\f\'\'\'\\left$

$\"\\\\f^4\\left$

Observe the pattern of the above derivatives.

From that , we can write general form of odd derivatives.

$\"D^{2k+1}(x\\sin$ .

Substitue $\"k=17\"$ in the above general form.

$\"\\\\D^{(2(17)+1)}(x\\sin$

Therefore,

$\"\\\\\\frac{d^{35}}{dx^{35}}(x\\sin$

$\"\"$

$\"\\\\\\frac{d^{35}}{dx^{35}}(x\\sin$