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Popular >

derivative of ln(x^5+8ln(x))

Solution

\frac{d}{d x} (ln (x^{5}) + 8 ln (x))

Solution

\frac{13}{x}

Solution steps

\frac{d}{d x} (ln (x^{5}) + 8 ln (x))

Simplify

ln (x^{5}) + 8 ln (x) : ln (x^{13})

= \frac{d}{d x} (ln (x^{13}))

Apply the chain rule:

\frac{1}{x ^{13}} \frac{d}{d x} (x^{13})

= \frac{1}{x ^{13}} \frac{d}{d x} (x^{13})

\frac{d}{d x} (x^{13}) = 13 x^{12}

= \frac{1}{x ^{13}} \cdot 13 x^{12}

Simplify

\frac{1}{x ^{13}} \cdot 13 x^{12} : \frac{13}{x}

= \frac{13}{x}

Popular Examples

tangent of f(x)=x^2+6x-16,\at x=2 tangent of

f (x) = x^{2} + 6 x - 16, at x = 2

limit as x approaches 0 of (h(x))/(g(x))

x \to 0 lim (\frac{h ( x )}{g ( x )})

derivative of (8x-x^2)^3 derivative of

(8 x - x^{2})^{3}

laplacetransform e^t*cos(t)+j*e^t*sin(t)laplace transform

e^{t} \cdot cos (t) + j \cdot e^{t} \cdot sin (t)

e^{x} d x = 2 y d y

Frequently Asked Questions (FAQ)

What is the derivative of ln(x^5+8ln(x)) ?
The derivative of ln(x^5+8ln(x)) is (13)/x
What is the first derivative of ln(x^5+8ln(x)) ?
The first derivative of ln(x^5+8ln(x)) is (13)/x