मराठी

Differentiate the following w.r.t. x: ex3 - Mathematics

Advertisements
Advertisements

प्रश्न

Differentiate the following w.r.t. x:

`e^(x^3)` 

बेरीज

उत्तर

Let, y = `e^(x^3)`

Differentiating both sides with respect to x,

`dy/dx = d/dx e^(x^3)`

`= e^(x^3) d/dx x^3`

`therefore  e^(x^3) * 3x^2 `

`= 3e^(x^3)*x^2`

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 5: Continuity and Differentiability - Exercise 5.4 [पृष्ठ १७४]

APPEARS IN

एनसीईआरटी Mathematics [English] Class 12
पाठ 5 Continuity and Differentiability
Exercise 5.4 | Q 3 | पृष्ठ १७४

संबंधित प्रश्‍न

Differentiate the following w.r.t. x:

`e^x/sinx`


Differentiate the following w.r.t. x: 

`e^(sin^(-1) x)`


Differentiate the following w.r.t. x: 

sin (tan–1 e–x)


Differentiate the following w.r.t. x:

`log(cos e^x)`


Differentiate the following w.r.t. x:

`e^x + e^(x^2) +... + e^(x^3)`


Differentiate the following w.r.t. x:

`sqrt(e^(sqrtx)), x > 0`


Differentiate the following w.r.t. x:

log (log x), x > 1


Differentiate the following w.r.t. x: 

`cos x/log x, x >0`


Differentiate the following w.r.t. x:

cos (log x + ex), x > 0


Differentiate w.r.t. x the function:

cos (a cos x + b sin x), for some constant a and b.


Using the fact that sin (A + B) = sin A cos B + cos A sin B and the differentiation, obtain the sum formula for cosines.


 If `"y" ="x"^"x" , "find"  "dy"/"dx"`.


If xy - yx = ab, find `(dy)/(dx)`.


If `"x" = "e"^(cos2"t")  "and"  "y" = "e"^(sin2"t")`, prove that `(d"y")/(d"x") = - ("y"log"x")/("x"log"y")`.


The derivative of log10x w.r.t. x is ______.


If yx = ey – x, prove that `"dy"/"dx" = (1 + log y)^2/logy`


If y = `(cos x)^((cos x)^((cosx)....oo)`, show that `"dy"/"dx" = (y^2 tanx)/(y log cos x - 1)`


Find `"dy"/"dx"`, if y = `x^tanx + sqrt((x^2 + 1)/2)`


If `"y" = ("x" + sqrt(1 + "x"^2))^"n",  "then" (1 + "x"^2)  ("d"^2 "y")/"dx"^2 + "x" ("dy")/("dx")` is ____________.


If `"y = a"^"x", "b"^(2"x" -1), "then" ("d"^2"y")/"dx"^2` is ____________.


If `"y" = (varphi "n x")/"x",` then the value of y'' (e) is ____________.


If `"x" = "a" ("cos"  theta + theta  "sin"  theta), "y = a" ("sin"  theta - theta  "cos"  theta), "then" ("d"^2 "y")/("dx"^2) =` ____________.


If `"xy"^2 = "ax"^2 + "bxy" + "y"^2, "then find"  "dy"/"dx"`


If `"y = tan"^-1 [("sin x + cos x")/("cos x - sin x")], "then"  "dy"/"dx"` is equal to ____________.


If f(x) = `"log"_("x"^2) ("log x")`, then f(e) is ____________.


The domain of the function defined by f(x) = logx 10 is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×