Advertisements
Advertisements
Question
Differentiate the following w. r. t. x. : ex log x
Advertisements
Solution
Let y = ex log x
Differentiating w.r.t. x, we get
`dy/dx = d/dx ("e"^xlog x)`
= `"e"^xd/dx(logx) + (logx) d/dx ("e"^x)`
=`"e"^x(1/x) + (logx)("e"^x)`
= `"e"^x(1/x+logx)`
APPEARS IN
RELATED QUESTIONS
Find the derivative of the following function w.r.t. x.:
x–9
Find the derivative of the following functions w. r. t. x.:
`x^(3/2)`
Differentiate the following w. r. t. x.: x5 + 3x4
Differentiate the following w. r. t. x. : `2/7 x^(7/2) + 5/2 x^(2/5)`
Differentiate the following w. r. t. x. : x3 log x
Find the derivative of the following w. r. t. x by using method of first principle:
x2 + 3x – 1
Find the derivative of the following w. r. t. x by using method of first principle:
3x
Find the derivative of the following w. r. t. x by using method of first principle:
`x sqrt(x)`
Show that the function f is not differentiable at x = −3, where f(x) `{:(= x^2 + 2, "for" x < - 3),(= 2 - 3x, "for" x ≥ - 3):}`
Show that f(x) = x2 is continuous and differentiable at x = 0
Discuss the continuity and differentiability of f(x) = x |x| at x = 0
Discuss the continuity and differentiability of f(x) = (2x + 3) |2x + 3| at x = `- 3/2`
Test the continuity and differentiability of f(x) `{:(= 3 x + 2, "if" x > 2),(= 12 - x^2, "if" x ≤ 2):}}` at x = 2
Select the correct answer from the given alternative:
If, f(x) = `x^50/50 + x^49/49 + x^48/48 + .... +x^2/2 + x + 1`, thef f'(1) =
Determine whether the following function is differentiable at x = 3 where,
f(x) `{:(= x^2 + 2"," , "for" x ≥ 3),(= 6x - 7"," , "for" x < 3):}`
Determine the values of p and q that make the function f(x) differentiable on R where
f(x) `{:( = "p"x^3",", "for" x < 2),(= x^2 + "q"",", "for" x ≥ 2):}`
Determine all real values of p and q that ensure the function
f(x) `{:( = "p"x + "q"",", "for" x ≤ 1),(= tan ((pix)/4)",", "for" 1 < x < 2):}` is differentiable at x = 1
Test whether the function f(x) `{:(= x^2 + 1",", "for" x ≥ 2),(= 2x + 1",", "for" x < 2):}` is differentiable at x = 2
