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
If y=2 cos(logx)+3 sin(logx), prove that `x^2(d^2y)/(dx2)+x dy/dx+y=0`
Find the second order derivative of the function.
ex sin 5x
Find the second order derivative of the function.
e6x cos 3x
Find the second order derivative of the function.
tan–1 x
Find the second order derivative of the function.
sin (log x)
If y = cos–1 x, find `(d^2y)/dx^2` in terms of y alone.
If y = 500e7x + 600e–7x, show that `(d^2y)/(dx^2)` = 49y.
If ey (x + 1) = 1, show that `(d^2y)/(dx^2) = (dy/dx)^2`.
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 = `"x"^-7`
Find `("d"^2"y")/"dx"^2`, if y = `"e"^"log x"`
Find `("d"^2"y")/"dx"^2`, if y = `"e"^((2"x" + 1))`.
Find `("d"^2"y")/"dx"^2`, if y = log (x).
`sin xy + x/y` = x2 – y
(x2 + y2)2 = xy
If ax2 + 2hxy + by2 + 2gx + 2fy + c = 0, then show that `"dy"/"dx" * "dx"/"dy"` = 1
If x sin (a + y) + sin a cos (a + y) = 0, prove that `"dy"/"dx" = (sin^2("a" + y))/sin"a"`
If y = tan–1x, find `("d"^2y)/("dx"^2)` in terms of y alone.
The derivative of cos–1(2x2 – 1) w.r.t. cos–1x is ______.
If x2 + y2 + sin y = 4, then the value of `(d^2y)/(dx^2)` at the point (–2, 0) is ______.
Let for i = 1, 2, 3, pi(x) be a polynomial of degree 2 in x, p'i(x) and p''i(x) be the first and second order derivatives of pi(x) respectively. Let,
A(x) = `[(p_1(x), p_1^'(x), p_1^('')(x)),(p_2(x), p_2^'(x), p_2^('')(x)),(p_3(x), p_3^'(x), p_3^('')(x))]`
and B(x) = [A(x)]T A(x). Then determinant of B(x) ______
If x = A cos 4t + B sin 4t, then `(d^2x)/(dt^2)` is equal to ______.
If x = a cos t and y = b sin t, then find `(d^2y)/(dx^2)`.
Read the following passage and answer the questions given below:
|
The relation between the height of the plant ('y' in cm) with respect to its exposure to the sunlight is governed by the following equation y = `4x - 1/2 x^2`, where 'x' is the number of days exposed to the sunlight, for x ≤ 3.
|
- Find the rate of growth of the plant with respect to the number of days exposed to the sunlight.
- Does the rate of growth of the plant increase or decrease in the first three days? What will be the height of the plant after 2 days?
Find `(d^2y)/dx^2` if, `y = e^((2x + 1))`
Find `(d^2y)/dx^2` if, y = `e^(2x +1)`
If y = 3 cos(log x) + 4 sin(log x), show that `x^2 (d^2y)/(dx^2) + x dy/dx + y = 0`
When is the second order derivative of \[y\] with respect to \[x\] defined?
Which of the following is NOT a stated notation for the second derivative of \[f(x)\]?
Higher order derivatives are obtained by which process?
Which equation is satisfied by \[y=\mathrm{A}\sin x+\mathrm{B}\cos x\]?
What is \[\frac{d}{dx}\left(\sqrt{1-x^2}\right)\] in the differentiation for \[y=\sin^{-1}x\]?
What equation is obtained after multiplying through by \[\sqrt{1-x^2}\] in the derivation for \[y=\sin^{-1}x\]?
For \[y=\sin^{-1}x\], which relation uses \[y_{1}\] for the first derivative?
