Differentiation Formulas

# Differentiation Formulas Video Lecture | Mathematics (Maths) for JEE Main & Advanced

## Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests

## FAQs on Differentiation Formulas Video Lecture - Mathematics (Maths) for JEE Main & Advanced

 1. What are the basic differentiation formulas used in JEE?
Ans. The basic differentiation formulas used in JEE include: - Constant Rule: $\frac{d}{dx}(c) = 0$, where $c$ is a constant. - Power Rule: $\frac{d}{dx}(x^n) = nx^{n-1}$, where $n$ is a real number. - Sum/Difference Rule: $\frac{d}{dx}(f(x) \pm g(x)) = \frac{d}{dx}(f(x)) \pm \frac{d}{dx}(g(x))$. - Product Rule: $\frac{d}{dx}(f(x)g(x)) = f'(x)g(x) + f(x)g'(x)$. - Quotient Rule: $\frac{d}{dx}\left(\frac{f(x)}{g(x)}\right) = \frac{f'(x)g(x) - f(x)g'(x)}{(g(x))^2}$.
 2. How do we differentiate exponential functions using differentiation formulas in JEE?
Ans. To differentiate exponential functions using differentiation formulas in JEE, we use the chain rule. The chain rule states that if we have a function of the form $f(g(x))$, then its derivative is given by $\frac{d}{dx}(f(g(x))) = f'(g(x)) \cdot g'(x)$. For example, to differentiate the function $f(x) = e^x$, we let $f(x) = e^x$ and $g(x) = x$. Then, using the chain rule, we have $\frac{d}{dx}(e^x) = \frac{d}{dx}(f(g(x))) = f'(g(x)) \cdot g'(x)$. Since the derivative of $e^x$ with respect to $x$ is $1$, we have $\frac{d}{dx}(e^x) = e^x \cdot 1 = e^x$.
 3. How can we differentiate trigonometric functions using differentiation formulas in JEE?
Ans. To differentiate trigonometric functions using differentiation formulas in JEE, we use the derivatives of the basic trigonometric functions. The derivatives of the basic trigonometric functions are as follows: - $\frac{d}{dx}(\sin x) = \cos x$ - $\frac{d}{dx}(\cos x) = -\sin x$ - $\frac{d}{dx}(\tan x) = \sec^2 x$ - $\frac{d}{dx}(\cot x) = -\csc^2 x$ - $\frac{d}{dx}(\sec x) = \sec x \cdot \tan x$ - $\frac{d}{dx}(\csc x) = -\csc x \cdot \cot x$ For example, to differentiate the function $f(x) = \sin x$, we have $\frac{d}{dx}(\sin x) = \cos x$.
 4. Can we differentiate logarithmic functions using differentiation formulas in JEE?
Ans. Yes, we can differentiate logarithmic functions using differentiation formulas in JEE. The derivative of the natural logarithmic function, $\ln x$, is $\frac{d}{dx}(\ln x) = \frac{1}{x}$. For example, to differentiate the function $f(x) = \ln x$, we have $\frac{d}{dx}(\ln x) = \frac{1}{x}$.
 5. Is there a differentiation formula for inverse trigonometric functions in JEE?
Ans. Yes, there are differentiation formulas for inverse trigonometric functions in JEE. The derivatives of the inverse trigonometric functions are as follows: - $\frac{d}{dx}(\arcsin x) = \frac{1}{\sqrt{1-x^2}}$ - $\frac{d}{dx}(\arccos x) = -\frac{1}{\sqrt{1-x^2}}$ - $\frac{d}{dx}(\arctan x) = \frac{1}{1+x^2}$ - $\frac{d}{dx}(\arccot x) = -\frac{1}{1+x^2}$ - $\frac{d}{dx}(\arcsec x) = \frac{1}{|x|\sqrt{x^2-1}}$ - $\frac{d}{dx}(\arccsc x) = -\frac{1}{|x|\sqrt{x^2-1}}$ For example, to differentiate the function $f(x) = \arcsin x$, we have $\frac{d}{dx}(\arcsin x) = \frac{1}{\sqrt{1-x^2}}$.

## Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests

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