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Popular >

derivative of (x-4/x+ln(x/4))

Solution

\frac{d}{d x} (\frac{x - 4}{x} + ln (\frac{x}{4}))

Solution

\frac{4}{x ^{2}} + \frac{1}{x}

Solution steps

\frac{d}{d x} (\frac{x - 4}{x} + ln (\frac{x}{4}))

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{x - 4}{x}) + \frac{d}{d x} (ln (\frac{x}{4}))

\frac{d}{d x} (\frac{x - 4}{x}) = \frac{4}{x ^{2}}

\frac{d}{d x} (ln (\frac{x}{4})) = \frac{1}{x}

= \frac{4}{x ^{2}} + \frac{1}{x}

Popular Examples

y^{''}-4y^'+3y=0,y(0)=1,y^'(0)= 1/3

y^{^{''}} - 4 y^{^{'}} + 3 y = 0, y (0) = 1, y^{^{'}} (0) = \frac{1}{3}

derivative of x^4+8x

\frac{d}{d x} (x^{4} + 8 x)

derivative of f(x)=-4/x derivative of

f (x) = - \frac{4}{x}

tangent of x^3,\at x=1 tangent of

x^{3}, at x = 1

derivative of y=(x^6-10)x derivative of

y = (x^{6} - 10) x

Frequently Asked Questions (FAQ)

What is the derivative of (x-4/x+ln(x/4)) ?
The derivative of (x-4/x+ln(x/4)) is 4/(x^2)+1/x
What is the first derivative of (x-4/x+ln(x/4)) ?
The first derivative of (x-4/x+ln(x/4)) is 4/(x^2)+1/x