How do you find the derivative of f(x)=5x arcsin(x)f(x)=5xarcsin(x)?

1 Answer
Jim G.
Aug 30, 2017

f'(x)=(5x)/(sqrt(1-x^2))+5arcsinx

Explanation:

"differentiate using the "color(blue)"product rule"

"given "f(x)=g(x)h(x)" then"

f'(x)=g(x)h'(x)+h(x)g'(x)larr" product rule"

g(x)=5xrArrg'(x)=5

h(x)=arcsinxrArrh'(x)=1/(sqrt(1-x^2))

rArrf'(x)=(5x)/(sqrt(1-x^2))+5arcsinx

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