Math  /  Calculus

QuestionFind the derivative of the function F(x)=ln(x4)F(x)=\ln \left(\frac{x}{4}\right).

Studdy Solution
Differentiate the simplified function with respect to x x . Recall that the derivative of ln(x)\ln(x) with respect to x x is 1x\frac{1}{x}, and the derivative of a constant is 00:
F(x)=ddx[ln(x)ln(4)] F'(x) = \frac{d}{dx}[\ln(x) - \ln(4)] F(x)=ddx[ln(x)]ddx[ln(4)] F'(x) = \frac{d}{dx}[\ln(x)] - \frac{d}{dx}[\ln(4)] F(x)=1x0 F'(x) = \frac{1}{x} - 0 F(x)=1x F'(x) = \frac{1}{x}
The derivative of the function F(x)=ln(x4) F(x) = \ln \left(\frac{x}{4}\right) is:
1x \boxed{\frac{1}{x}}

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