Advertisements
Advertisements
Question
Differentiate the following w. r. t. x. : `sqrtx (x^2 + 1)^2`
Solution
Let y = `sqrtx (x^2 + 1)^2`
∴ `y = x^(1/2) (x^4 + 2x^2 + 1)`
y = `x^(9/2) + 2x^(5/2) + x^(1/2)`
Differentiating w.r.t. x, we get
`dy/dx = d/dx (x^(9/2) + 2x^(5/2) + x^(1/2))`
= `d/dx x^(9/2) + 2d/dxx^(5/2) + d/dxsqrtx`
= `9/2 x^(9/2-1) + 2xx 5/2 x^(5/2-1)+1/(2sqrtx)`
= `9/2 x^(7/2) + 5x^(3/2) + 1/(2sqrtx)`
APPEARS IN
RELATED QUESTIONS
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:
e2x+1
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. 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:
`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`
Discuss the continuity and differentiability of f(x) at x = 2
f(x) = [x] if x ∈ [0, 4). [where [*] is a greatest integer (floor) function]
Examine the function
f(x) `{:(= x^2 cos (1/x)",", "for" x ≠ 0),(= 0",", "for" x = 0):}`
for continuity and differentiability at x = 0
Select the correct answer from the given alternative:
If y = `("a"x + "b")/("c"x + "d")`, then `("d"y)/("d"x)` =
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):}`
Discuss whether the function f(x) = |x + 1| + |x – 1| is differentiable ∀ x ∈ R
Test whether the function f(x) `{:(= x^2 + 1",", "for" x ≥ 2),(= 2x + 1",", "for" x < 2):}` is differentiable at x = 2
If y = `"e"^x/sqrt(x)` find `("d"y)/("d"x)` when x = 1
