Differential Calculus Important formulas
Differentiation Formulas for Calculus
If you are studying derivatives in calculus, here are some differentiation formulas you need to know:
The derivative of a constant is always zero.
The power rule states that the derivative of a function with a variable raised to a constant is that
constant times the variable raised to the n minus 1. For instance, the derivative of x cubed is 3x squared.
The derivative of a constant raised to a variable is a to the x times ln a.
The constant multiple rule states that the derivative of a function multiplied by a constant c is that
constant times the derivative of the function.
The product rule states that the derivative of the product of two functions is the derivative of the first
function times the second function plus the first function times the derivative of the second function.
The quotient rule states that the derivative of a fraction of two functions is (v u prime - u v prime) over v
squared.
The chain rule is used to find the derivative of a composite function, and it involves differentiating the
outer function, keeping the inside part the same, multiplying by the derivative of the inside part, and
then multiplying by the derivative of the inside function.
The derivative of logarithmic functions depends on the base, and the derivative of trig functions involves
the use of the chain rule.
The inverse trig formulas also require the use of the chain rule, and the derivative of the inverse sine of
u is u prime over the square root of 1 minus u squared.
To learn more about logarithmic differentiation and see examples of these formulas in action, check out
the links in the description below.
Derivatives of Inverse Trig Functions
Calculating the derivatives of inverse trigonometric functions can be similar to finding the derivatives of
their corresponding trig functions. The only difference is that there may be a negative sign involved.
Let's take a look at some of the most common formulas:
The derivative of inverse sine of u is equal to u prime over the square root of 1 minus u squared.
Differentiation Formulas for Calculus
If you are studying derivatives in calculus, here are some differentiation formulas you need to know:
The derivative of a constant is always zero.
The power rule states that the derivative of a function with a variable raised to a constant is that
constant times the variable raised to the n minus 1. For instance, the derivative of x cubed is 3x squared.
The derivative of a constant raised to a variable is a to the x times ln a.
The constant multiple rule states that the derivative of a function multiplied by a constant c is that
constant times the derivative of the function.
The product rule states that the derivative of the product of two functions is the derivative of the first
function times the second function plus the first function times the derivative of the second function.
The quotient rule states that the derivative of a fraction of two functions is (v u prime - u v prime) over v
squared.
The chain rule is used to find the derivative of a composite function, and it involves differentiating the
outer function, keeping the inside part the same, multiplying by the derivative of the inside part, and
then multiplying by the derivative of the inside function.
The derivative of logarithmic functions depends on the base, and the derivative of trig functions involves
the use of the chain rule.
The inverse trig formulas also require the use of the chain rule, and the derivative of the inverse sine of
u is u prime over the square root of 1 minus u squared.
To learn more about logarithmic differentiation and see examples of these formulas in action, check out
the links in the description below.
Derivatives of Inverse Trig Functions
Calculating the derivatives of inverse trigonometric functions can be similar to finding the derivatives of
their corresponding trig functions. The only difference is that there may be a negative sign involved.
Let's take a look at some of the most common formulas:
The derivative of inverse sine of u is equal to u prime over the square root of 1 minus u squared.
