How do you find the derivative of $f (x) = {log}_{x} (3)$ $f(x) = log_x (3)$ ?

Question

How do you find the derivative of $f (x) = {log}_{x} (3)$ $f(x) = log_x (3)$ ?

1 Answer

Impact of this question

1456 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-06-01T20:15:10

$\frac{d f}{d x} (x) = - \frac{{log}_{e} 3}{x {log}_{e}^{2} (x)}$ $(df)/(dx)(x) = -log_e3/(x log_e^2(x))$

Explanation:

$y = {log}_{x} 3 = \frac{{log}_{b} 3}{{log}_{b} x}$ $y = log_x 3 = (log_b 3)/(log_b x)$ for any convenient basis $b$ $b$

Calling now $g (x, y) = y {log}_{e} x - {log}_{e} 3 = 0$ $g(x,y) = y log_e x - log_e 3 = 0$ after taking $b = e$ $b = e$ , we have

$d g = g_{x} d x + g_{y} d y = 0$ $dg = g_x dx + g_y dy = 0$

then

$\frac{d y}{d x} = - \frac{g_{x}}{g_{y}} = - \frac{(\frac{y}{x})}{{log}_{e} x} = - \frac{y}{x {log}_{e} (x)} = - \frac{{log}_{e} 3}{x {log}_{e}^{2} (x)}$ $(dy)/(dx) = - (g_x)/(g_y) = -((y/x))/(log_e x) = -y/(x log_e(x)) = -log_e3/(x log_e^2(x))$

Science

Math

Humanities

... and beyond

How do you find the derivative of $f (x) = {log}_{x} (3)$ $f(x) = log_x (3)$ ?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you find the derivative of f(x)=logx(3)f(x) = log_x (3)?

1 Answer

Explanation:

Related questions

Impact of this question

How do you find the derivative of $f (x) = {log}_{x} (3)$ $f(x) = log_x (3)$ ?