English

If y = x10, then dydx is ______ - Mathematics and Statistics

Advertisements
Advertisements

Question

If y = x10, then `("d"y)/("d"x)` is ______

Fill in the Blanks
Advertisements

Solution

10x9 

shaalaa.com
  Is there an error in this question or solution?
Chapter 1.3: Differentiation - Q.2

RELATED QUESTIONS

if `y = tan^2(log x^3)`, find `(dy)/(dx)`


Find `"dy"/"dx"` if cos (xy) = x + y


Find `"dy"/"dx"` if, y = `"a"^((1 + log "x"))`


Choose the correct alternative.

If y = (5x3 - 4x2 - 8x)9, then `"dy"/"dx"` =


Fill in the Blank.

If 3x2y + 3xy2 = 0, then `(dy)/(dx)` = ______.


Solve the following:

If y = (6x3 - 3x2 - 9x)10, find `"dy"/"dx"` 


Find `"dy"/"dx"`, if y = `2^("x"^"x")`.


If f'(4) = 5, f(4) = 3, g'(6) = 7 and R(x) = g[3 + f(x)] then R'(4) = ______


Choose the correct alternative:

If y = `x^(sqrt(x))`, then `("d"y)/("d"x)` = ?


If y = (5x3 – 4x2 – 8x)9, then `("d"y)/("d"x)` is ______


State whether the following statement is True or False:

If y = ex, then `("d"y)/("d"x)` = ex 


y = (6x4 – 5x3 + 2x + 3)6, find `("d"y)/("d"x)`

Solution: Given,

y = (6x4 – 5x3 + 2x + 3)6 

Let u = `[6x^4 - 5x^3 + square + 3]`

∴ y = `"u"^square`

∴ `("d"y)/"du"` = 6u6–1

∴ `("d"y)/"du"` = 6(  )5 

and `"du"/("d"x) = 24x^3 - 15(square) + 2`

By chain rule,

`("d"y)/("d"x) = ("d"y)/square xx square/("d"x)`

∴ `("d"y)/("d"x) = 6(6x^4 - 5x^3 + 2x + 3)^square xx (24x^3 - 15x^2 + square)`


If y = `x/"e"^(1 + x)`, then `("d"y)/("d"x)` = ______.


Derivative of ex sin x w.r.t. e-x cos x is ______.


If ex + ey = ex+y , prove that `("d"y)/("d"x) = -"e"^(y - x)`


If f(x) = |cos x – sinx|, find `"f'"(pi/6)`


Let f(x) = log x + x3 and let g(x) be the inverse of f(x), then |64g"(1)| is equal to ______.


If y = em sin–1 x and (1 – x2) = Ay2, then A is equal to ______.


If y = `root5((3x^2 + 8x + 5)^4)`, find `dy/dx`


Find the rate of change of demand (x) of acommodity with respect to its price (y) if

`y = 12 + 10x + 25x^2`


lf y = f(u) is a differentiable function of u and u = g(x) is a differentiable function of x, such that the composite function y = f[g(x)] is a differentiable function of x, then prove that:

`dy/dx = dy/(du) xx (du)/dx`

Hence, find `d/dx[log(x^5 + 4)]`.


If x = Φ(t) is a differentiable function of t, then prove that:

`int f(x)dx = int f[Φ(t)]*Φ^'(t)dt`

Hence, find `int(logx)^n/x dx`.


If y = `sqrt((1 - x)/(1 + x))`, then `(1 - x^2) dy/dx + y` = ______.


Find `dy/dx` if, y = `e^(5x^2 - 2x + 4)`


If y = `root5((3x^2+8x+5)^4)`, find `dy/dx`


Solve the following:

If `y =root(5)((3x^2 + 8x + 5)^4), "find" dy/(dx)`


If `y=root5((3x^2+8x+5)^4)`, find `dy/dx`


If `y = root{5}{(3x^2 + 8x + 5)^4}, "find"  dy/dx`.


If y = `root{5}{(3x^2 + 8x + 5)^4)`, find `(dy)/(dx)`


Find `dy/dx` if, `y = e^(5x^2 - 2x +  4)`.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×