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find dy/dx if `y=tan^-1((6x)/(1-5x^2))`
Concept: Derivative of Inverse Function
If `y=sec^-1((sqrtx-1)/(x+sqrtx))+sin_1((x+sqrtx)/(sqrtx-1)), `
(A) x
(B) 1/x
(C) 1
(D) 0
Concept: Derivative of Inverse Function
If x = f(t), y = g(t) are differentiable functions of parammeter ‘ t ’ then prove that y is a differentiable function of 'x' and hence, find dy/dx if x=a cost, y=a sint
Concept: Derivatives of Functions in Parametric Forms
If x=at2, y= 2at , then find dy/dx.
Concept: Derivatives of Functions in Parametric Forms
If `x=a(t-1/t),y=a(t+1/t)`, then show that `dy/dx=x/y`
Concept: Derivatives of Functions in Parametric Forms
If `ax^2+2hxy+by^2=0` , show that `(d^2y)/(dx^2)=0`
Concept: Derivatives of Functions in Parametric Forms
If y =1 − cos θ, x = 1 − sin θ, then `dy/dx "at" θ =pi/4` is ______
Concept: Derivatives of Functions in Parametric Forms
If x=α sin 2t (1 + cos 2t) and y=β cos 2t (1−cos 2t), show that `dy/dx=β/αtan t`
Concept: Derivatives of Functions in Parametric Forms
Find the value of `dy/dx " at " theta =pi/4 if x=ae^theta (sintheta-costheta) and y=ae^theta(sintheta+cos theta)`
Concept: Derivatives of Functions in Parametric Forms
If x = cos t (3 – 2 cos2 t) and y = sin t (3 – 2 sin2 t), find the value of dx/dy at t =4/π.
Concept: Derivatives of Functions in Parametric Forms
Derivatives of tan3θ with respect to sec3θ at θ=π/3 is
(A)` 3/2`
(B) `sqrt3/2`
(C) `1/2`
(D) `-sqrt3/2`
Concept: Derivatives of Functions in Parametric Forms
If y = f (x) is a differentiable function of x such that inverse function x = f –1(y) exists, then
prove that x is a differentiable function of y and
`dx/dy=1/(dy/dx)`, Where `dy/dxne0`
Hence if `y=sin^-1x, -1<=x<=1 , -pi/2<=y<=pi/2`
then show that `dy/dx=1/sqrt(1-x^2)`, where `|x|<1`
Concept: Derivative of Inverse Function
If `x = acos^3t`, `y = asin^3 t`,
Show that `(dy)/(dx) =- (y/x)^(1/3)`
Concept: Derivatives of Functions in Parametric Forms
Find `dy/dx` if `y = tan^(-1) ((5x+ 1)/(3-x-6x^2))`
Concept: Derivative of Inverse Function
If X = f(t) and Y = g(t) Are Differentiable Functions of t , then prove that y is a differentiable function of x and
`"dy"/"dx" =("dy"/"dt")/("dx"/"dt" ) , "where" "dx"/"dt" ≠ 0`
Hence find `"dy"/"dx"` if x = a cos2 t and y = a sin2 t.
Concept: Derivatives of Functions in Parametric Forms
If y = sin -1 `((8x)/(1 + 16x^2))`, find `(dy)/(dx)`
Concept: Derivatives of Functions in Parametric Forms
The total cost function of a firm is C = x2 + 75x + 1600 for output x. Find the output for which the average cost ls minimum. Is CA= Cm at this output?
Concept: Derivative of Inverse Function
Differentiate the following w.r.t.x:
tan[cos(sinx)]
Concept: Introduction & Derivatives of Some Standard Functions
Differentiate the following w.r.t. x: `x^(tan^(-1)x`
Concept: Introduction & Derivatives of Some Standard Functions
Differentiate the following w.r.t. x: xe + xx + ex + ee.
Concept: Introduction & Derivatives of Some Standard Functions
