Home
Class 12
MATHS
If f(x)=x|x|, then prove that f^(prime)(...

If `f(x)=x|x|,` then prove that `f^(prime)(x)=2|x|`

Text Solution

Verified by Experts

`f(x)=x|x|, ne 0`
`rArr" "f(x)={:{(-x^(2), x lt 0),(x^(2), x gt 0):}`
`rArr" "f'(x)={:{(-2"x,","" x lt 0),(2"x,",""x gt 0):}`
`therefore" "f'(x)=2|x|, x ne 0`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Solved Examples|28 Videos

  • DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Concept Application 3.1|1 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|578 Videos

  • DOT PRODUCT

    CENGAGE PUBLICATION|Exercise DPP 2.1|15 Videos

Similar Questions

Explore conceptually related problems

If f(x)=x|x| , prove that f'(x)=2|x|

If f(x)=x|x|,prove that f'(x)=2|x|.

A function f: R->R satisfies the equation f(x+y)=f(x)f(y) for all x , y in R and f(x)!=0 for all x in Rdot If f(x) is differentiable at x=0a n df^(prime)(0)=2, then prove that f^(prime)(x)=2f(x)dot

If f(x) = x|x| , prove that f'(1) = 2 .

If f(x)=(1-x)/(1+x) , then prove that f(x)+f(1/x)=0 .

If 2f(x-1)-f((1-x)/x)=x , then prove that 3f(x)=2(x+1)+1/(x+1) .

If f(x)=4^(x) , then prove that (f(x+1))/(f(x-1))=16 .

If f(x)=5^x , then prove : (f(x+1))/(f(x-1))=25

If f(x)=5^x , then prove : f(log_5x)=x

If f(x)=2^(x) , then prove that f(x +1) = 4f( x - 1).