Let f(x) be a differentiable and let c a...

Let `f(x)` be a differentiable and let `c` a be a constant. Then `cf(x)` is also differentiable such that `d/(dx){cf(x)}=c d/(dx)(f(x))dot`

Topper's Solved these Questions

COMPLEX NUMBERS
RD SHARMA ENGLISH|Exercise All Questions|269 Videos
ELLIPSE
RD SHARMA ENGLISH|Exercise All Questions|100 Videos

Similar Questions

Explore conceptually related problems

If f(x)a n dg(x) a re differentiate functions, then show that f(x)+-g(x) are also differentiable such that d/(dx){f(x)+-g(x)}=d/(dx){f(x)}+-d/(dx){g(x)}

If f(x)a n dg(x) are two differentiable functions, show that f(x)g(x) is also differentiable such that d/(dx)[f(x)g(x)]=f(x)d/(dx){g(x)}+g(x)d/(dx){f(x)}

If f(x)a n dg(f) are two differentiable functions and g(x)!=0 , then show trht (f(x))/(g(x)) is also differentiable d/(dx){(f(x))/(g(x))}=(g(x)d/x{f(x)}-g(x)d/x{g(x)})/([g(x)]^2)

Let f(x)=a+b|x|+c|x|^4 , where a ,\ b , and c are real constants. Then, f(x) is differentiable at x=0 , if a=0 (b) b=0 (c) c=0 (d) none of these

Let f(x)=a+b|x|+c|x|^4 , where a , ba n dc are real constants. Then, f(x) is differentiable at x=0, if a=0 (b) b=0 (c) c=0 (d) none of these

Let f(x)=|x| and g(x)=|x^3|, then (a) f(x)a n dg(x) both are continuous at x=0 (b) f(x)a n dg(x) both are differentiable at x=0 (c) f(x) is differentiable but g(x) is not differentiable at x=0 (d) f(x) and g(x) both are not differentiable at x=0

f(x) is differentiable function and (f(x).g(x)) is differentiable at x = a . Then (a) g(x) must be differentiable at x=a (b.) if g(x) is discontinuous, then f(a)=0 (c.) if f(a)!=0 , then g(x) must be differentiable (d.) none of these

The function f(x)=e^x+x , being differentiable and one-to-one, has a differentiable inverse f^(-1)(x)dot The value of d/(dx)(f^(-1)) at the point f(log2) is (a) 1/(1n2) (b) 1/3 (c) 1/4 (d) none of these

The function f(x)=e^x+x , being differentiable and one-to-one, has a differentiable inverse f^(-1)(x)dot The value of d/(dx)(f^(-1)) at the point f(log2) is 1/(1n2) (b) 1/3 (c) 1/4 (d) none of these

Using first principles, prove that d/(dx){1/(f(x))}=-(f^(prime)(x))/({f(x)}^2)

RD SHARMA ENGLISH-DERIVATIVES-All Questions

The differentiation of e^x with respect to xi se^xdot i.e. d/(dx)(e^x...
Text Solution
|
Differentiate the following functions with respect to x : (log)xx ...
Text Solution
|
Let f(x) be a differentiable and let c a be a constant. Then cf(x) is ...
Text Solution
|
Differentiate the following functions with respect to x : (sqrt(x...
Text Solution
|
Differentiate the following functions with respect to x : (3x)/(x+t...
Text Solution
|
Differentiate the following functions with respect to x : (10^x)/(s...
Text Solution
|
Differentiate the following functions with respect to x : x^2e^x...
Text Solution
|
Differentiate the following functions with respect to x (i)(2x+3)/(...
Text Solution
|
If y=1+x/(1!)+(x^2)/(2!)+(x^3)/(3!)++(x^n)/(n !), show that (dy)/(dx)...
Text Solution
|
If y=1+x/(1!)+(x^2)/(2!)+(x^3)/(3!)+ , show that (dy)/(dx)=ydot
Text Solution
|
Differentiate the following functions with respect to x : x^4(5sinx-...
Text Solution
|
Differentiate the following functions with respect to x : (xsinx+cos...
Text Solution
|
Differentiate the following functions with respect to x : (e^x+sinx...
Text Solution
|
Differentiate the following functions with respect to x : (e^x-tanx...
Text Solution
|
The differentiation of cosx with respect to x' is -sinxdot i.e. d/(dx...
Text Solution
|
The differentiation of s inx with respect to xi scosxdot i.e. d/(dx)(...
Text Solution
|
Differentiate logsinx from the first principles.
Text Solution
|
Find the derivative of sin x3 from first principles.
Text Solution
|
The differentiation of y=a^x.
Text Solution
|
Differentiate e^(sqrt(tanx)) from the first principle.
Text Solution
|