Advertisements
Advertisements
Question
Differentiate the following w.r.t. x:
`e^(x^3)`
Advertisements
Solution
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`
= `e^(x^3) * 3x^2 `
= `3e^(x^3)*x^2`
APPEARS IN
RELATED QUESTIONS
Differentiate 3x w.r.t. log3x
Differentiate the following w.r.t. x:
`e^x/sinx`
Differentiate the following w.r.t. x:
log (cos ex)
Differentiate the following w.r.t. x:
`sqrt(e^(sqrtx))`, x > 0
Differentiate the following w.r.t. x:
cos (log x + ex), x > 0
Differentiate the function with respect to x:
(log x)log x, x > 1
Differentiate the function with respect to x:
cos (a cos x + b sin x), for some constant a and b.
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")`.
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 `"y"^2 = "ax"^2 + "bx + c", "then" "d"/"dx" ("y"^3 "y"_"z") =` ____________.
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
Which function is an exponential function?
What is \[\frac{d}{dx}(e^x)\]?
Which expression gives the change of base rule?
Which expression gives the quotient rule for logarithms?
Which expression gives the power rule for logarithms?
What is the domain of the exponential function \[y=b^x\]?
What is the range of the logarithmic function \[y=\log_b x\]?
Through which point does every graph of \[y=\log_b x\] pass?
The graph of \[y=\log_b x\] is a mirror image of which graph reflected perfectly across \[y=x\]?
If \[y=b^x\], which equivalent logarithmic statement is correct?
For \[x>0\], differentiate \[\sin(\log x)\] with respect to \[x\].
Differentiate \[\cos^{-1}(e^x)\] with respect to \[x\].
Differentiate \[e^{\cos x}\] with respect to \[x\].
Which list contains the main log laws?
