Advertisements
Advertisements
प्रश्न
Differentiate the following:
h(t) = `("t" - 1/"t")^(3/2)`
Advertisements
उत्तर
h(t) = `("t" - 1/"t")^(3/2)`
[y = f(g(x)
`("d"y)/("d"x)` = f'(g(x)) . g'(x)]
h'(t) = `3/2 ("t" - 1/"t")^(3/2 - 1) "d"/"dt" ("t" - 1/"t")`
= `3/2 (1 - 1/"t")^(1/2) [ 1 - (- 1) "t"^(-1 - 1)]`
= `3/2 ("t" - 1/"t")^(1/2) (1 + "t"^(-2))`
h'(t) = `3/2 ("t" - 1/"t")^(1/2) (1 + 1/"t"^2)`
APPEARS IN
संबंधित प्रश्न
Find the derivatives of the following functions with respect to corresponding independent variables:
f(x) = x – 3 sin x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `sinx/(1 + cosx)`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = cosec x . cot x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = log10 x
Find the derivatives of the following functions with respect to corresponding independent variables:
Draw the function f'(x) if f(x) = 2x2 – 5x + 3
Differentiate the following:
F(x) = (x3 + 4x)7
Differentiate the following:
y = (2x – 5)4 (8x2 – 5)–3
Differentiate the following:
y = `(x^2 + 1) root(3)(x^2 + 2)`
Differentiate the following:
y = `5^((-1)/x)`
Differentiate the following:
y = (1 + cos2)6
Differentiate the following:
y = `"e"^(xcosx)`
Differentiate the following:
y = `sin^-1 ((1 - x^2)/(1 + x^2))`
Find the derivatives of the following:
y = `x^(logx) + (logx)^x`
Find the derivatives of the following:
`sqrt(x) = "e"^((x - y))`
Find the derivatives of the following:
`tan^-1sqrt((1 - cos x)/(1 + cos x)`
Find the derivatives of the following:
Find the derivative of `sin^-1 ((2x)/(1 + x^2))` with respect to `tan^-1 x`
Find the derivatives of the following:
If x = a(θ + sin θ), y = a(1 – cos θ) then prove that at θ = `pi/2`, yn = `1/"a"`
Choose the correct alternative:
The differential coefficient of `log_10 x` with respect to `log_x 10` is
Choose the correct alternative:
If y = `(1 - x)^2/x^2`, then `("d"y)/("d"x)` is
Choose the correct alternative:
If f(x) = `{{:(x - 5, "if" x ≤ 1),(4x^2 - 9, "if" 1 < x < 2),(3x + 4, "if" x ≥ 2):}` , then the right hand derivative of f(x) at x = 2 is
