Differentiation Formula Class 12

Differentiation Formula Class 12 holds great importance in calculus to solve differential equations problems. In addition to mathematics, these formulas are also useful in real life situations to solve practical problems. However, when the logic behind differentiation formulas is not clear there are higher chances of miscalculations and errors. Therefore, students must carefully memorize these formulas and important concepts related to them. To help students with their learning this article gives the list of important differentiation formula class 12 at one place with solved examples.

List of Differentiation Formula Class 12

• If f and g are two real functions that are continuous at a real number c, then

(i) f + g is continuous at x = c.

(ii) f – g is continuous at x = c.

(iii) f . g is continuous at x = c.

(iv) f/ g is continuous at x = c, (provided g (c) ≠ 0)

• Suppose f and g are real valued functions such that (f o g) is defined at c. If g is continuous at c and if f is continuous at g (c), then (f o g) is continuous at c.

• d/dx (sin^-1 x) = 1/√1-x2
• d/dx (cos^-1 x) = - 1/√1-x2
• d/dx (tan^-1 x) = 1/√1 + x2
• d/dx (cot^-1 x) = -1/√1 + x2
• d/dx (sec^-1 x) = 1/√x1-x2
• d/dx (sin^-1 x) = 1/√1-x2
• d/dx (cosec^-1 x) = - 1/√1-x2
• d/dx (e^-x) = e^-x
• d/dxlog x = 1/x

Applications of Differentiation Formula Class 12

Differentiation formula find their usage in various subjects and domains such as physics, seismology, business, science, economics and social science. Some of the useful applications of Differentiation formula class 12 are listed below :

• Differentiation formulas are used in many engineering and science problems for simulating the behavior of moving objects.
• In geography, these formulas are applied to study the properties of gases present in the atmosphere.
• In business, differentiation formulas are applied to calculate the profit and loss using graphs.

Tips to Memorize Differentiation Formula Class 12

Here are some tips that the students can follow to memorize the differentiation formula class 12 formulas effectively:

• Students should get familiar with all the basic concepts and terms used in differentiation formulas to apply them with ease.
• Practicing problems based on differentiation formula will help in building the right problem-solving approach. By solving various problems based on differentiation formulas students can learn to apply the formulas in the right sequence.
• Students should understand the derivation of the differentiation formula to understand its logic. Learning formulas logically is also necessary to apply them in complex problem-solving.
• Students can take the help of study material available online such as formula sheets and explanatory videos to understand and memorize formulas.

Differentiation Formula Class 12 Examples

Example 1: Verify if function f(x) = sin x² is a continuous function.

Solution 1: For a function to be continuous it should have a value for every real value of input (x)

We know that function g(x) = sin x is a continuous function.

Also, we know that function h(x) = x² is also a continuous function.

We know that “If g is continuous at c and if f is continuous at g (c), then (f o g) is continuous at c.”

Thus, since both g(x) and h(x) are continuous functions, f(x) = sin x² is also continuous.

Example 2 : Differentiate function f(x) = c^x, where ‘c’ is a constant greater than zero.

Solution : Let t = c^x , taking log at both sides:

log (t) = x log c

Differentiating both ends with respect to ‘x’:

1/t dt/dx = log c

dt/dx = t log c

d/dx c^x = c^x log c

Students can download the printable Maths Formulas Class 12 sheet from below.