# Recent questions tagged derivatives

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### Find the derivative of $\large\frac{2}{x+1}$$- \large\frac{x^2}{3x-1} ### Find the derivative of x^{-4}(3-4x^{-5}) ### Find the derivative of x^5(3-6x^{-9}) ### Find the derivative of x^{-3}(5+3x) ### Find the derivative of (5x^3+3x-1)(x-1) ### Find the derivative of 2x-\large\frac{3}{4} ### Find the derivative of \large\frac{x^n-a^n}{x-a} for some constant a ### For some constants a and b, find the derivative of  \large\frac{(x-a)}{(x-b)} ### For some constants a and b, find the derivative of  (ax^2+b)^2 ### For some constants a and b, find the derivative of  (x-a)(x-b) ### Find the derivatives of x^n+ax^{n-1}+a^2x^{n-2}+...+a^{n-1}x+a^n for some fixed real number a ### For the function  f(x) = \large\frac{x^{100}}{100}$$+ \large\frac{x^{99}}{99}$$+...+\large\frac{x^2}{2}$$+x+1$ then $f'(1) is ### Find the derivative of the given function from first principle $ \Large\frac{x+1}{x-1}$### Find the derivative of the given function from first principle $\Large\frac{1}{x^2}$. ### Find the derivative of the given function from first principle $(x-1)(x-2)$### Find the derivative of the given function from first principle $x^3-27$### Find the derivative of$x$at$ x = 1$. ### Find the derivative of$99x$at$ x = 100$. ### Find the derivative of$x^2-2$at$ x = 10$### Let$f(a)=g(a)=k$and their$n^{th}$derivatives$f^{(n)}(a),g^{(n)}(a)$exist and are not equal for some n. Further if$\lim\limits_{x\to a}\large\frac{f(a)g(x)-f(a)-g(a)f(x)+g(a)}{g(x)-f(x)}$$=4 then the value of K is ### If f(x)=\cot^{-1}\big[\large\frac{3x-x^3}{1-3x^2}\big] and g(x)=\cos^{-1}\big[\large\frac{1-x^2}{1+x^2}\big] then \lim\limits_{x\to a}\large\frac{f(x)-f(a)}{g(x)-g(a)}$$\quad0 < a < \large\frac{1}{2}$is ### Let$f(x+y)=f(x)f(y)\forall x,y\in R$. Suppose that$f(3)=3$and$f'(0)=11$, then$f'(3)$is given by ###$f(x)$is the integral of$\large\frac{2\sin x-\sin 2x}{x^3}$$x\neq 0 find \lim\limits_{x\to 0}f'(x) ### Let f(a)=g(a)=k and their n^{th} derivatives f^n(a), g^n(a) exist and are not equal for some n. Further if \lim\limits_{x\to a}\large\frac{f(a)g(x)-f(a)-g(a)f(x)+f(a)}{g(x)-f(x)}$$=4$, then the value of k is ### The left hand derivative of$f(x)=[x]\sin(\pi x)$at$x=k$, where$k$is an integer is ### If$f(x)=\left\{\begin{array}{1 1}\large\frac{\sin [x]}{[x]}&[x]\neq 0\\0&[x]=0\end{array}\right.$, where$[x]$denotes the greatest integer less than or equal to x, then$\lim\limits_{x\to 0}f(x)$equals ### If$f(a)=2$,$f'(a)=1$,$g(a)=-1$,$g'(a)=2$, then the value of$\lim\limits_{x\to a}\large\frac{g(x)f(a)-g(a)f(x)}{x-a}$is ###$\lim\limits_{h\to 0}\large\frac{ln(1+2h)-2ln(1+h)}{h^2}=$### If$f(x)=\large\frac{1}{\sqrt{18-x^2}}$then$\lim\limits_{x\to 3}\large\frac{f(x)-f(3)}{x-3}$is ### If$f(9)=9,f'(9)=4$then$\lim\limits_{x\to 9}\large\frac{\sqrt{f(x)}-3}{\sqrt x-3}$is ### If$f(5)=15,f'(5)=3$then$\lim\limits_{x\to 5}\large\frac{xf(5)-5f'(x)}{x-5}$is ### Evaluate :$\lim\limits_{h\to 0}\large\frac{(a+h)^2\sin(a+h)-a^2\sin a}{h}$### For$x\in R\lim\limits_{x\to \infty}\big(\large\frac{x-3}{x+2}\big)^x\$=

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