Math virtual assistant

About Snapxam Calculators Topics Go Premium
ENGESP

Logarithmic differentiation Calculator

Get detailed step by step solutions to your math problems with our online calculator. Sharpen your math skills and learn step by step with our math solver. Check out more calculators here.

Go!
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
2

e
π
ln
log
lim
d/dx
d/dx
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

1

Example

$\frac{d}{dx}\left(\ln\left(x\sqrt{a+x}\right)\right)$
2

The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If $f(x)=ln\:a$ (where $a$ is a function of $x$), then $\displaystyle f'(x)=\frac{a'}{a}$

$\frac{1}{\sqrt{x+a}x}\cdot\frac{d}{dx}\left(\sqrt{x+a}x\right)$
3

Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=x$ and $g=\sqrt{x+a}$

$\frac{1}{\sqrt{x+a}x}\left(x\frac{d}{dx}\left(\sqrt{x+a}\right)+\sqrt{x+a}\cdot\frac{d}{dx}\left(x\right)\right)$
4

The derivative of the linear function is equal to $1$

$\frac{1}{\sqrt{x+a}x}\left(x\frac{d}{dx}\left(\sqrt{x+a}\right)+\sqrt{x+a}\right)$
5

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$\frac{1}{\sqrt{x+a}x}\left(\frac{1}{2}x\left(x+a\right)^{-\frac{1}{2}}\cdot\frac{d}{dx}\left(x+a\right)+\sqrt{x+a}\right)$
6

The derivative of a sum of two functions is the sum of the derivatives of each function

$\frac{1}{\sqrt{x+a}x}\left(\frac{1}{2}x\left(x+a\right)^{-\frac{1}{2}}\left(\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(a\right)\right)+\sqrt{x+a}\right)$
7

The derivative of the constant function is equal to zero

$\frac{1}{\sqrt{x+a}x}\left(\frac{1}{2}x\left(x+a\right)^{-\frac{1}{2}}\left(\frac{d}{dx}\left(x\right)+0\right)+\sqrt{x+a}\right)$
8

The derivative of the linear function is equal to $1$

$\left(\left(1+0\right)\cdot \frac{1}{2}x\left(x+a\right)^{-\frac{1}{2}}+\sqrt{x+a}\right)\frac{1}{\sqrt{x+a}x}$
9

Add the values $0$ and $1$

$\left(1\cdot \frac{1}{2}x\left(x+a\right)^{-\frac{1}{2}}+\sqrt{x+a}\right)\frac{1}{\sqrt{x+a}x}$
10

Multiply $\frac{1}{2}$ times $1$

$\left(\frac{1}{2}x\left(x+a\right)^{-\frac{1}{2}}+\sqrt{x+a}\right)\frac{1}{\sqrt{x+a}x}$
11

Multiplying the fraction and term

$\frac{\frac{1}{2}x\left(x+a\right)^{-\frac{1}{2}}+\sqrt{x+a}}{\sqrt{x+a}x}$
12

Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number

$\frac{\frac{1}{2}x\frac{1}{\sqrt{x+a}}+\sqrt{x+a}}{\sqrt{x+a}x}$
13

Apply the formula: $a\frac{1}{x}$$=\frac{a}{x}$, where $a=\frac{1}{2}$ and $x=\sqrt{x+a}$

$\frac{x\frac{\frac{1}{2}}{\sqrt{x+a}}+\sqrt{x+a}}{\sqrt{x+a}x}$
14

Multiplying the fraction and term

$\frac{\frac{\frac{1}{2}x}{\sqrt{x+a}}+\sqrt{x+a}}{\sqrt{x+a}x}$
15

Apply the formula: $\frac{b}{c}+a$$=\frac{b+c\cdot a}{c}$, where $a=\sqrt{x+a}$, $b=\frac{1}{2}x$ and $c=\sqrt{x+a}$

$\frac{\frac{\frac{1}{2}x+\sqrt{x+a}\sqrt{x+a}}{\sqrt{x+a}}}{\sqrt{x+a}x}$
16

When multiplying exponents with same base we can add the exponents

$\frac{\frac{\frac{1}{2}x+x+a}{\sqrt{x+a}}}{\sqrt{x+a}x}$
17

Adding $\frac{1}{2}x$ and $x$

$\frac{\frac{a+\frac{3}{2}x}{\sqrt{x+a}}}{\sqrt{x+a}x}$
18

Simplifying the fraction

$\frac{a+\frac{3}{2}x}{\sqrt{x+a}\sqrt{x+a}x}$
19

When multiplying exponents with same base we can add the exponents

$\frac{a+\frac{3}{2}x}{x\left(x+a\right)}$
20

Multiplying polynomials $x$ and $a+x$

$\frac{a+\frac{3}{2}x}{x^2+a\cdot x}$