First Derivative Calculator(Solver) with Steps

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

* is multiplication; it can be left out: 2x, x sin(x), (x+1)(x-2).
x^2 is $x^2$, x^(1/3) is $x^{\frac13}$ and e^(2x) is $e^{2x}$.
sqrt(x) is $\sqrt{x}$ and sqrt[3](x) is $\sqrt[3]{x}$.
(a+b)/(c+d) is $\frac{a+b}{c+d}$. Put the numerator and the denominator in brackets.
ln(x) or log(x) is the natural logarithm; log_2(x) is $\log_2 x$.
sin(x), cos(x), tan(x), cot(x), sec(x), csc(x); sin^2(x) is $\sin^2(x)$.
arcsin(x), arccos(x), arctan(x), arccot(x); sinh(x), cosh(x), tanh(x).
pi is $\pi$, e is the number $e$ and |x| is the absolute value.
The variable is $x$. If there is no $x$, another letter is taken: the derivative of t^2 is found with respect to $t$. The other letters are constants.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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