Advertisements
Advertisements
प्रश्न
Differentiate the following w. r. t. x. : ex log x
Advertisements
उत्तर
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
संबंधित प्रश्न
Find the derivative of the following function w.r.t. x.:
x–9
Find the derivative of the following function w. r. t. x.:
`7xsqrt x`
Find the derivative of the following function w. r. t. x.:
35
Differentiate the following w. r. t. x.: x5 + 3x4
Differentiate the following w. r. t. x. : `x^(5/2) + 5x^(7/5)`
Differentiate the following w. r. t. x. : x3 log x
Differentiate the following w. r. t. x. : x3 .3x
Find the derivative of the following w. r. t. x by using method of first principle:
tan (2x + 3)
Find the derivative of the following w. r. t. x by using method of first principle:
sec (5x − 2)
Find the derivative of the following w. r. t. x. at the point indicated against them by using method of first principle:
`sqrt(2x + 5)` at x = 2
Find the derivative of the following w. r. t. x. at the point indicated against them by using method of first principle:
tan x at x = `pi/4`
Find the derivative of the following w. r. t. x. at the point indicated against them by using method of first principle:
`2^(3x + 1)` at x = 2
Find the derivative of the following w. r. t. x. at the point indicated against them by using method of first principle:
cos x at x = `(5pi)/4`
Show that f(x) = x2 is continuous and differentiable at x = 0
Discuss the continuity and differentiability of f(x) = (2x + 3) |2x + 3| at x = `- 3/2`
Examine the function
f(x) `{:(= x^2 cos (1/x)",", "for" x ≠ 0),(= 0",", "for" x = 0):}`
for continuity and differentiability at x = 0
Test whether the function f(x) `{:(= x^2 + 1",", "for" x ≥ 2),(= 2x + 1",", "for" x < 2):}` is differentiable at x = 2
