Asked by Beth
s(x)=log3(x^2+6x) find derivative?
Answers
Answered by
Steve
if u = f(x)
and y = g(u)
dy/dx = dy/du * du/dx
y = log3(u)
u = x^2 + 6x
dy/dx = 1/ln3 * 1/u * du/dx
= 1/ln3 * 1/(x^2 + 6x) * (2x+6)
= (2x+6)/(ln 3 * (x^2 + 6x))
and y = g(u)
dy/dx = dy/du * du/dx
y = log3(u)
u = x^2 + 6x
dy/dx = 1/ln3 * 1/u * du/dx
= 1/ln3 * 1/(x^2 + 6x) * (2x+6)
= (2x+6)/(ln 3 * (x^2 + 6x))
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