Advertisements
Advertisements
Question
State whether the following is True or False:
The derivative of `"x"^"m"*"y"^"n" = ("x + y")^("m + n")` is `"x"/"y"`
Options
True
False
Advertisements
Solution
False
APPEARS IN
RELATED QUESTIONS
Find `bb(dy/dx)` in the following:
2x + 3y = sin x
Find `bb(dy/dx)` in the following:
xy + y2 = tan x + y
Show that the derivative of the function f given by
Examine the differentialibilty of the function f defined by
\[f\left( x \right) = \begin{cases}2x + 3 & \text { if }- 3 \leq x \leq - 2 \\ \begin{array}xx + 1 \\ x + 2\end{array} & \begin{array} i\text { if } - 2 \leq x < 0 \\\text { if } 0 \leq x \leq 1\end{array}\end{cases}\]
If y = `sqrt(cosx + sqrt(cosx + sqrt(cosx + ... ∞)`, then show that `"dy"/"dx" = sinx/(1 - 2y)`.
Find `"dy"/"dx"` if x = at2, y = 2at.
Find `"dy"/"dx"` if : x = a cos3θ, y = a sin3θ at θ = `pi/(3)`
If x = `(t + 1)/(t - 1), y = (t - 1)/(t + 1), "then show that" y^2 + "dy"/"dx"` = 0.
Differentiate `tan^-1((x)/(sqrt(1 - x^2))) w.r.t. sec^-1((1)/(2x^2 - 1))`.
Find `(d^2y)/(dx^2)` of the following : x = sinθ, y = sin3θ at θ = `pi/(2)`
Find the nth derivative of the following : eax+b
Choose the correct option from the given alternatives :
If y = sec (tan –1x), then `"dy"/"dx"` at x = 1, is equal to
Choose the correct option from the given alternatives :
If y = `a cos (logx) and "A"(d^2y)/(dx^2) + "B""dy"/"dx" + "C"` = 0, then the values of A, B, C are
Differentiate log `[(sqrt(1 + x^2) + x)/(sqrt(1 + x^2 - x)]]` w.r.t. cos (log x).
If y2 = a2cos2x + b2sin2x, show that `y + (d^2y)/(dx^2) = (a^2b^2)/y^3`
Choose the correct alternative.
If y = 5x . x5, then `"dy"/"dx" = ?`
Choose the correct alternative.
If x = `("e"^"t" + "e"^-"t")/2, "y" = ("e"^"t" - "e"^-"t")/2` then `"dy"/"dx"` = ?
If x2 + y2 = t + `1/"t"` and x4 + y4 = t2 + `1/"t"^2` then `("d"y)/("d"x)` = ______
If y = `sqrt(tansqrt(x)`, find `("d"y)/("d"x)`.
If x = sin θ, y = tan θ, then find `("d"y)/("d"x)`.
`(dy)/(dx)` of `xy + y^2 = tan x + y` is
y = `e^(x3)`
If y = y(x) is an implicit function of x such that loge(x + y) = 4xy, then `(d^2y)/(dx^2)` at x = 0 is equal to ______.
Find `dy/dx` if, x = e3t, y = `e^sqrtt`
Find `dy/dx` if, `x = e^(3t), y = e^sqrtt`
If log(x + y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`
