# First Derivative Calculator(Solver) with Steps

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

Function

1. Differentiate $$- 2300 x + \frac{2600 x}{x + 1} + 12000$$ term by term:

1. The derivative of the constant $$12000$$ 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: $$x$$ goes to $$1$$

So, the result is: $$-2300$$

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:

$$f{\left (x \right )} = x$$ and $$g{\left (x \right )} = x + 1$$.

To find $$\frac{d}{d x} f{\left (x \right )}$$:

1. Apply the power rule: $$x$$ goes to $$1$$

To find $$\frac{d}{d x} g{\left (x \right )}$$:

1. Differentiate $$x + 1$$ term by term:

1. The derivative of the constant $$1$$ is zero.

2. Apply the power rule: $$x$$ goes to $$1$$

The result is: $$1$$

Now plug in to the quotient rule:

$$\frac{1}{\left(x + 1\right)^{2}}$$

So, the result is: $$\frac{2600}{\left(x + 1\right)^{2}}$$

The result is: $$-2300 + \frac{2600}{\left(x + 1\right)^{2}}$$

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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