Advertisements
Advertisements
प्रश्न
Differentiate the following w. r. t. x. : ex log x
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 functions w. r. t. x.:
`x^(3/2)`
Find the derivative of the following function w. r. t. x.:
`7xsqrt x`
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. : `sqrtx (x^2 + 1)^2`
Differentiate the following w. r. t. x. : `x^(5/2) e^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:
sin (3x)
Find the derivative of the following w. r. t. x by using method of first principle:
e2x+1
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 by using method of first principle:
`x sqrt(x)`
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`
Discuss the continuity and differentiability of f(x) = x |x| at x = 0
If f(x) `{:(= sin x - cos x, "if" x ≤ pi/2),(= 2x - pi + 1, "if" x > pi /2):}` Test the continuity and differentiability of f at x = `π/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
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 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
Discuss whether the function f(x) = |x + 1| + |x – 1| is differentiable ∀ x ∈ R