Advertisements
Advertisements
प्रश्न
Differentiate the following:
y = (x2 + 4x + 6)5
Advertisements
उत्तर
Let = u = x2 + 4x + 6
⇒ `("d"u)/("d"x)` = 2x + 4
Now y = u5
⇒ `("d"y)/("d"x)` = 5u4
∴ `("d"y)/("d"x) = ("d"y)/("d"x) xx ("d"u)/("d"x)` = 5u4 (2x + 4)
= 5(x2 + 4x + 6)4 (2x + 4)
= 5(2x + 4) (x2 + 4x + 6)4
APPEARS IN
संबंधित प्रश्न
Find the derivatives of the following functions with respect to corresponding independent variables:
f(x) = x sin x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = tan θ (sin θ + cos θ)
Differentiate the following:
y = `"e"^sqrt(x)`
Differentiate the following:
y = `(sin^2x)/cos x`
Differentiate the following:
y = `5^((-1)/x)`
Differentiate the following:
y = (1 + cos2)6
Differentiate the following:
y = `sin(tan(sqrt(sinx)))`
Find the derivatives of the following:
y = `x^(logx) + (logx)^x`
Find the derivatives of the following:
`sqrt(x^2 + y^2) = tan^-1 (y/x)`
Find the derivatives of the following:
`tan^-1 = ((6x)/(1 - 9x^2))`
Find the derivatives of the following:
x = `(1 - "t"^2)/(1 + "t"^2)`, y = `(2"t")/(1 + "t"^2)`
Find the derivatives of the following:
sin-1 (3x – 4x3)
Find the derivatives of the following:
`tan^-1 ((cos x + sin x)/(cos x - sin x))`
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:
Find the derivative with `tan^-1 ((sinx)/(1 + cos x))` with respect to `tan^-1 ((cosx)/(1 + sinx))`
Find the derivatives of the following:
If y = `(sin^-1 x)/sqrt(1 - x^2)`, show that (1 – x2)y2 – 3xy1 – y = 0
