Derivative is a rate of change of function with respect to a variable.After the invention of a derivative of a function by Newton and Leibnitz in around 17th century, it is widely used in the sector of math and physics.
Some of the important formulas of derivative are as follows:-
Let u, v, and w are functions of the variable x, and a, b, c are constant then
Derivative of Trigonometric function and their inverse:
Derivative of the Exponential and Logarithmic
Deviate of the Hyperbolic function and their Inverses
Recall the definition of the trigonometric functions of the trigonometric functions.
Higher Order Derivatives
Let y = f(x) we have:
Second derivative is :
Third Derivative is:
nth Derivative is:
in some books, the following notation for higher derivatives is also used:
Higher Derivative formula for the product: Leibniz formula
Application of Derivatives
a. Volume of Cone(V) = , r = radius, h= height
b. Volume of Cylinder (V) =
c. Volume of Sphere(V) =
d. Surface area of Sphere(S) =
e. Curved surface of Cylinder(S) =
f. Total surface area of Cylinder (S) =
ii. Equation of tangent at is
iii. Equation of normal at is
iv. Let and be the slope of tangents to the two curves and be the angle between them, then,
v. Approximate increase in y is
vi. Actual increase in y in
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