First Derivative Calculator(Solver) with Steps

Free derivatives calculator(solver) that gets the detailed solution of the first derivative of a function.

[tex]\frac{d}{d x}\left(- 2300 x + \frac{2600 x}{x + 1} + 12000\right)[/tex]

Differentiate [tex]- 2300 x + \frac{2600 x}{x + 1} + 12000[/tex] term by term:
1. The derivative of the constant [tex]12000[/tex] is zero.
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: [tex]x[/tex] goes to [tex]1[/tex]
  So, the result is: [tex]-2300[/tex]
3. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the quotient rule, which is:
    
    [tex]\frac{d}{d x}\left(\frac{f{\left (x \right )}}{g{\left (x \right )}}\right) = \frac{1}{g^{2}{\left (x \right )}} \left(- f{\left (x \right )} \frac{d}{d x} g{\left (x \right )} + g{\left (x \right )} \frac{d}{d x} f{\left (x \right )}\right)[/tex]
    
    [tex]f{\left (x \right )} = x[/tex] and [tex]g{\left (x \right )} = x + 1[/tex].
    
    To find [tex]\frac{d}{d x} f{\left (x \right )}[/tex]:
    1. Apply the power rule: [tex]x[/tex] goes to [tex]1[/tex]
    To find [tex]\frac{d}{d x} g{\left (x \right )}[/tex]:
    1. Differentiate [tex]x + 1[/tex] term by term:
      1. The derivative of the constant [tex]1[/tex] is zero.
      2. Apply the power rule: [tex]x[/tex] goes to [tex]1[/tex]
      The result is: [tex]1[/tex]
    Now plug in to the quotient rule:
    
    [tex]\frac{1}{\left(x + 1\right)^{2}}[/tex]
  So, the result is: [tex]\frac{2600}{\left(x + 1\right)^{2}}[/tex]
The result is: [tex]-2300 + \frac{2600}{\left(x + 1\right)^{2}}[/tex]

The answer is:

[tex]-2300 + \frac{2600}{\left(x + 1\right)^{2}}[/tex]

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Commands:
* is multiplication
oo is $\infty$
pi is $\pi$
x^2 is x²
sqrt(x) is $\sqrt{x}$
sqrt[3](x) is $\sqrt[3]{x}$
(a+b)/(c+d) is $\frac{a+b}{c+d}$

The Most Important Derivatives - Basic Formulas/Rules

$\frac{d}{dx}a=0$ (a is a constant)

$\frac{d}{dx}x=1$

$\frac{d}{dx}x^n=nx^{n-1}$

$\frac{d}{dx}e^x=e^x$

$\frac{d}{dx}\log x=\frac1x$

$\frac{d}{dx}a^x=a^x\log x$

$(f\ g)' = f'g + fg'$ - Product Rule

$(\frac{f}{g})' = \frac{f'g - fg'}{g^2}$ - Quotient Rule

$\frac{d}{dx}f(g(x)) = f'(g(x))g'(x)$ - Chain Rule

$\frac{d}{dx}\sin(x)=\cos(x)$

$\frac{d}{dx}\cos(x)=-\sin(x)$

$\frac{d}{dx}\tan(x)=\sec^2(x)$

$\frac{d}{dx}\cot(x)=-csc^2(x)$

$\frac{d}{dx}\arcsin(x)=\frac{1}{\sqrt{1-x^2}}$

$\frac{d}{dx}\arccos(x)=-\frac{1}{\sqrt{1-x^2}}$

$\frac{d}{dx}\arctan(x)=\frac{1}{1+x^2}$

$\frac{d}{dx}\text{arccot}(x)=-\frac{1}{1+x^2}$

$\frac{d}{dx}\text{arcsec}(x)=\frac{1}{x\sqrt{x^2-1}}$

$\frac{d}{dx}\text{arccsc}(x)=-\frac{1}{x\sqrt{x^2-1}}$

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Definition of a derivative Problems Calculus - forum

First Derivative Calculator(Solver) with Steps

Answer:

The Most Important Derivatives - Basic Formulas/Rules

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