Advertisements
Advertisements
प्रश्न
If y=eax ,show that `xdy/dx=ylogy`
Advertisements
उत्तर
`y=e^(ax)`
`y=e^(ax) ...............(i)`
`logy=ax..............(ii)`
`dy/dx=ae^(ax)`
`dy/dx=ay`
`xdy/dx=axy `
`xdy/dx=ylogy `
APPEARS IN
संबंधित प्रश्न
if `x^y + y^x = a^b`then Find `dy/dx`
Show that the derivative of the function f given by
Find `(dy)/(dx)` if `y = sin^-1(sqrt(1-x^2))`
Discuss extreme values of the function f(x) = x.logx
Find `"dy"/"dx"` if x = at2, y = 2at.
Find `"dy"/"dx"`, if : x = `sqrt(a^2 + m^2), y = log(a^2 + m^2)`
Find `"dy"/"dx"`, if : `x = cos^-1((2t)/(1 + t^2)), y = sec^-1(sqrt(1 + t^2))`
If x = at2 and y = 2at, then show that `xy(d^2y)/(dx^2) + a` = 0.
If y = `e^(mtan^-1x)`, show that `(1 + x^2)(d^2y)/(dx^2) + (2x - m)"dy"/"dx"` = 0.
If x = cos t, y = emt, show that `(1 - x^2)(d^2y)/(dx^2) - x"dy"/"dx" - m^2y` = 0.
If y = sin (m cos–1x), then show that `(1 - x^2)(d^2y)/(dx^2) - x"dy"/"dx" + m^2y` = 0.
Find the nth derivative of the following : (ax + b)m
Find the nth derivative of the following : cos x
Find the nth derivative of the following : sin (ax + b)
Find the nth derivative of the following : cos (3 – 2x)
Find the nth derivative of the following : y = eax . cos (bx + c)
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 = sin (2sin–1 x), then dx = ........
Choose the correct option from the given alternatives :
If `xsqrt(y + 1) + ysqrt(x + 1) = 0 and x ≠ y, "then" "dy"/"dx"` = ........
Choose the correct option from the given alternatives :
If x = a(cosθ + θ sinθ), y = a(sinθ – θ cosθ), then `((d^2y)/dx^2)_(θ = pi/4)` = .........
Differentiate the following w.r.t. x : `cos^-1((sqrt(1 + x) - sqrt(1 - x))/2)`
Differentiate the following w.r.t. x:
`tan^-1(x/(1 + 6x^2)) + cot^-1((1 - 10x^2)/(7x))`
If x = `e^(x/y)`, then show that `dy/dx = (x - y)/(xlogx)`
DIfferentiate `tan^-1((sqrt(1 + x^2) - 1)/x) w.r.t. tan^-1(sqrt((2xsqrt(1 - x^2))/(1 - 2x^2)))`.
Differentiate `tan^-1((sqrt(1 + x^2) - 1)/x)` w.r.t. `cos^-1(sqrt((1 + sqrt(1 + x^2))/(2sqrt(1 + x^2))))`
If x= a cos θ, y = b sin θ, show that `a^2[y(d^2y)/(dx^2) + (dy/dx)^2] + b^2` = 0.
Find `"dy"/"dx"` if, x3 + y3 + 4x3y = 0
Find `"dy"/"dx"` if, x3 + x2y + xy2 + y3 = 81
If `x^7 * y^9 = (x + y)^16`, then show that `dy/dx = y/x`
If x = sin θ, y = tan θ, then find `("d"y)/("d"x)`.
y = `e^(x3)`
If log(x + y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`
If log(x + y) = log(xy) + a then show that, `dy/dx = (-y^2)/x^2`
Find `dy/dx` if, x = `e^(3t)`, y = `e^sqrtt`
Find `dy/dx` if, x = e3t, y = `e^sqrtt`
If log(x + y) = log(xy) + a then show that, `dy/dx = (−y^2)/x^2`
Find `dy/(dx) "if" , x = e^(3t), y = e^sqrtt`.
