Advertisements
Advertisements
प्रश्न
Differentiate the following:
F(x) = (x3 + 4x)7
उत्तर
F(x) = (x3 + 4x)7
[y = f(g(x)
`("d"y)/("d"x)` = f'(g(x)) . g'(x)]
F'(x) = `7(x^3 + 4x)^(7 - 1) "d"/("d"x) (x^3 + 4x)`
= 7(x3 + 4x)6 (3x2 + 4)
= 7(3x2 + 4)(x3 + 4x)6
APPEARS IN
संबंधित प्रश्न
Find the derivatives of the following functions with respect to corresponding independent variables:
y = cosec x . cot x
Differentiate the following:
y = cos (tan x)
Differentiate the following:
y = sin (ex)
Differentiate the following:
f(t) = `root(3)(1 + tan "t")`
Differentiate the following:
y = 4 sec 5x
Differentiate the following:
y = `(x^2 + 1) root(3)(x^2 + 2)`
Differentiate the following:
s(t) = `root(4)(("t"^3 + 1)/("t"^3 - 1)`
Differentiate the following:
f(x) = `x/sqrt(7 - 3x)`
Differentiate the following:
y = sin2(cos kx)
Find the derivatives of the following:
tan (x + y) + tan (x – y) = x
Find the derivatives of the following:
`tan^-1sqrt((1 - cos x)/(1 + cos x)`
Find the derivatives of the following:
`cos[2tan^-1 sqrt((1 - x)/(1 + x))]`
Find the derivatives of the following:
x = a (cos t + t sin t); y = a (sin t – t cos t)
Find the derivatives of the following:
Find the derivative of sin x2 with respect to x2
Find the derivatives of the following:
If u = `tan^-1 (sqrt(1 + x^2) - 1)/x` and v = `tan^-1 x`, find `("d"u)/("d"v)`
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:
If the derivative of (ax – 5)e3x at x = 0 is – 13, then the value of a is
Choose the correct alternative:
If f(x) = `{{:(2"a" - x, "for" - "a" < x < "a"),(3x - 2"a", "for" x ≥ "a"):}` , then which one of the following is true?
