Enter the function, select the variable, add the order of derivation, and click the calculate button to find the derivation.
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Use this derivative calculator to find the derivatives of various functions with one, multiple variables, and complex types. You can easily differentiate functions up to 5 orders and get the step-by-step solution with this online derivative solver.
Use the derivative rules for finding the derivatives of the given mathematical functions:
Constant Rule:
The derivative of the constant is equal to zero.
Example:
f(x) = 4
f’(x) = 0
Constant Multiple Rule:
Taking the derivative first and then multiplying by the constant has the same effect as multiplying by the constant first and then taking the derivative of the function.
(cf(x))′ =c(f(x))′
Example:
(4x2)′=4(x2)′=4⋅2x=8x
Example:
\(\ (𝑥^4)′=\ 3𝑥^{4−1}=3𝑥^{3}\)
Performing the derivative of the sum of two functions is equal to the sum of both function's derivatives. (f(x)+g(x))′=f′(x)+g′(x)
Example:
(x2+7x)′=(x2)′+(7x)′=2x+7.
The derivative of the two functions product is equal to the sum of the derivative of both functions. (f(x)g(x))′=f′(x)g(x)+f(x)g′(x)
Example:
(x sin(x))′=(x)′sin(x)+x(sin(x))′=sin(x)+xcos(x)
\((\frac{f(x)}{g(x)})'= \frac{f'(x)g(x)-f(x)g'(x)}{g^{2}(x)}\)
Example:
\((\frac {x} {y} )' = \frac {xy' - x'y} {y^2}\)
According to Chain Rule, the derivation of
\(\ f(g(x)) =\ f '(g(x))g'(x)\)
According to Reciprocal Rule, the derivative of
\(\frac {1} {w} = \frac {-fw'} {w^2}\)
Function | Derivative | |
---|---|---|
Constant | c | 0 |
Line | x | 1 |
ax | a | |
Square | x^{2} | 2x |
Square Root | √x | (½)x^{-½} |
Exponential | e^{x} | e^{x} |
a^{x} | ln(a) a^{x} | |
Logarithms | ln(x) | 1/x |
log_{a}(x) | 1 / (x ln(a)) | |
Trigonometry (x is in radians) | sin(x) | cos(x) |
cos(x) | −sin(x) | |
tan(x) | sec^{2}(x) | |
Inverse Trigonometry | sin^{-1}(x) | 1/√(1−x^{2}) |
cos^{-1}(x) | −1/√(1−x^{2}) | |
tan^{-1}(x) | 1/(1+x^{2}) |
Apart from common functions, you can add functions to our derivative calculator and let it provide step-by-step derivation.
A few applications of derivatives are:
Typically No, for most of the functions (polynomials, trig functions, etc.) order of the derivative does not affect the answer. However, for functions with sharp jumps (like absolute value), where high order derivative might not be continuous the order of the derivative matters.
The first derivative tells you the slope (steepness), but the second derivative measures the rate of change of the first derivative. The second derivative demonstrates the increase or decrease in the slope of the tangent line.
The second derivative is the differentiation of the first derivative of a function. The double derivative calculator lets you simplify second or higher-order derivatives and shows each step how to do it.
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