Advertisements
Advertisements
प्रश्न
sec(x + y) = xy
Advertisements
उत्तर
Given that: sec(x + y) = xy
Differentiating both sides w.r.t. x
`"d"/"dx" sec(x + y) = "d"/"dx"(xy)`
⇒ `sec(x + y) tan(x + y) * "d"/"dx"(x + y) = x*"dy"/"dx" + y*1`
⇒ `sec(x + y)*tan(x + y) (1 + "dy"/"dx") = x*"dy"/"dx" + y`
⇒ `sec(x + y)*tan(x + y) + sec(x + y)*"dy"/"dx"` = y – sec(x + y).tan(x + y)
⇒ `[sec(x + y)* tan(x + y) - x] "dy"/"dx"` = = y – sec(x + y).tan(x + y)
⇒ `"dy"/"dx" = (y - sec(x + y)*tan(x + y))/(sec(x + y)*tan(x + y) - x)`
Hence, `"dy"/"dx" = (y - sec(x + y)*tan(x + y))/(sec(x + y)*tan(x + y) - x)`.
APPEARS IN
संबंधित प्रश्न
Find the second order derivative of the function.
ex sin 5x
Find the second order derivative of the function.
tan–1 x
Find the second order derivative of the function.
log (log x)
If y = 3 cos (log x) + 4 sin (log x), show that x2y2 + xy1 + y = 0.
If y = 500e7x + 600e–7x, show that `(d^2y)/(dx^2)` = 49y.
If y = (tan–1 x)2, show that (x2 + 1)2 y2 + 2x (x2 + 1) y1 = 2
Find `("d"^2"y")/"dx"^2`, if y = `"x"^5`
Find `("d"^2"y")/"dx"^2`, if y = `"e"^"log x"`
Find `("d"^2"y")/"dx"^2`, if y = `"e"^((2"x" + 1))`.
If x2 + 6xy + y2 = 10, then show that `("d"^2y)/("d"x^2) = 80/(3x + y)^3`
If ax2 + 2hxy + by2 = 0, then show that `("d"^2"y")/"dx"^2` = 0
`sin xy + x/y` = x2 – y
tan–1(x2 + y2) = a
(x2 + y2)2 = xy
If y = tan–1x, find `("d"^2y)/("dx"^2)` in terms of y alone.
Derivative of cot x° with respect to x is ____________.
If x = A cos 4t + B sin 4t, then `(d^2x)/(dt^2)` is equal to ______.
If y = tan x + sec x then prove that `(d^2y)/(dx^2) = cosx/(1 - sinx)^2`.
If x = a cos t and y = b sin t, then find `(d^2y)/(dx^2)`.
Find `(d^2y)/(dx^2)` if, y = `e^((2x+1))`
Find `(d^2y)/dx^2` if, y = `e^((2x + 1))`
Find `(d^2y)/dx^2 "if," y= e^((2x+1))`
Find `(d^2y)/dx^2` if, `y = e^((2x + 1))`
Let \[y=f(x)\]. What is the first derivative of \[y\] with respect to \[x\]?
Which expression defines the second order derivative of \[y\] with respect to \[x\]?
Higher order derivatives are obtained by which process?
If \[y=\mathrm{A}\sin x+\mathrm{B}\cos x\], what is \[\frac{dy}{dx}\]?
For \[y=\mathrm{A}\sin x+\mathrm{B}\cos x\], what is \[\frac{d^2y}{dx^2}\]?
Which equation is satisfied by \[y=\mathrm{A}\sin x+\mathrm{B}\cos x\]?
After differentiating \[\sqrt{1-x^2}\cdot\frac{dy}{dx}=1\], which equation results?
Differentiating \[(1-x^2)y_{1}^{2}=1\] gives which expression?
Which equation follows from \[(1-x^2)\cdot2y_{1}y_{2}+y_{1}^{2}(0-2x)=0\]?
