e Diff Problem

[Jason76]

Product Rule:

Given: \(\displaystyle f(x) g(x)\)

\(\displaystyle g(x)[f'(x)] + f(x)[g'(x)]\)

\(\displaystyle f(x) = 3xe^{x}\csc(x)\)

\(\displaystyle f'(x) = \csc(x) [\dfrac{d}{dx} 3xe^{x} ] + 3xe^{x}[\dfrac{d}{dx} \csc(x) ]\)

\(\displaystyle f'(x) = \tan(x)[3xe^{x}] + 3xe^{x}[-\csc(x)\cot(x)]\)

\(\displaystyle f'(x) = \tan(x)[3xe^{x}] + [-3xe^{x} \csc(x)\cot(x)]\)

\(\displaystyle f'(x) = \tan(x)[3xe^{x}] - 3xe^{x} \csc(x)\cot(x)\) :?:

 

[Deleted member 4993]

Product Rule:

Given: \(\displaystyle f(x) g(x)\)................Incorrect ................ here you are dealing with f(x) = u(x) * v(x) * w(x)

then

f'(x) = u'(x) * v(x) * w(x) + u(x) * v'(x) * w(x) + u(x) * v(x) * w'(x)

Redo your problem