Advertisements
Advertisements
Question
Differentiate the following:
y = (2x – 5)4 (8x2 – 5)–3
Advertisements
Solution
y = (2x – 5)4 (8x2 – 5)–3
`("d"y)/("d"x) = (2x - 5)^4 xx "d"/("d"x) (8x^2 - 5)^(-3) + (8x^2 - 5)^(-3) xx "d"/("d"x) (2x - 5)^4` .......(By product rule)
`("d"y)/("d"x) = (2x - 5)^4 xx - 3(8x^2 - 5)^(- 3 - 1) (8 xx 2x - 0) + (8x^2 - 5)^(-3) xx 4(2x - 5)^(4 - 1) (2 xx 1 - 0)`
`("d"y)/("d"x) = - 3(2x - 5)^4 (8x^2 - 5)^(-4) xx 16x + (8x^2 - 5)^(-3) xx 4(2x - 5)^3 (2 xx 1)`
`("d"y)/("d"x) = - 48x (2x - 5)^4 (8x^2 - 5)^(- 4) + 8(8x^2 - 5)^(- 3) (2x - 5)^3`
= `-48x (2x - 5)^4 xx 1/(8x^2 - 5)^4 + (8(2x - 5)^3)/(8x^2 - 5)^3`
= `(8(2x - 5)^3)/(8x^2 - 5)^3 [1 - (6x(2x - 5))/(8x^2 - 5)]`
= `(8(2x - 5)^3)/(8x^2 - 5)^3 xx [(8x^2 - 5 - 12x^2 + 30x)/(8x^2 - 5)]`
= `(8(2x - 5)^3)/(8x^2 - 5)^3 xx [- 4x^2 + 30x - 5]`
`("d"y)/("d"x) = (8(2x - 5)^3)/(8x^2 - 5)^4 xx (30x - 4x^2 - 5)`
APPEARS IN
RELATED QUESTIONS
Find the derivatives of the following functions with respect to corresponding independent variables:
y = cos x – 2 tan x
Find the derivatives of the following functions with respect to corresponding independent variables:
y = `sinx/x^2`
Find the derivatives of the following functions with respect to corresponding independent variables:
y = x sin x cos 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:
y = tan 3x
Differentiate the following:
y = `"e"^sqrt(x)`
Differentiate the following:
s(t) = `root(4)(("t"^3 + 1)/("t"^3 - 1)`
Differentiate the following:
y = tan (cos x)
Differentiate the following:
y = `sqrt(1 + 2tanx)`
Differentiate the following:
y = (1 + cos2)6
Differentiate the following:
y = `"e"^(3x)/(1 + "e"^x`
Differentiate the following:
y = `sin^-1 ((1 - x^2)/(1 + x^2))`
Find the derivatives of the following:
`sqrt(x^2 + y^2) = tan^-1 (y/x)`
Find the derivatives of the following:
`cos[2tan^-1 sqrt((1 - x)/(1 + x))]`
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 with `tan^-1 ((sinx)/(1 + cos x))` with respect to `tan^-1 ((cosx)/(1 + sinx))`
Choose the correct alternative:
`"d"/("d"x) ("e"^(x + 5log x))` is
