Question

3/5*[(2x^2-7x-5)^5]^1/3 find the derivative​

Answer 1

we have to differentiate \sqrt[3/5]{(2x^2-7x-5)^5}

3/5

(2x

2

−7x−5)

5

with respect to x .

first resolve the function into simpler form,

\sqrt[3/5]{(2x^2-7x-5)^5}=(2x^2-7x-5)^{5\times\frac{3}{5}}

3/5

(2x

2

−7x−5)

5

=(2x

2

−7x−5)

5×

5

3

= (2x^2-7x-5)^3(2x

2

−7x−5)

3

now let y = (2x²- 7x - 5)³

differentiating y with respect to x,

dy/dx = 3(2x² - 7x - 5)³¯¹ d(2x² - 7x - 5)/dx

= 3(2x² - 7x - 5)²(4x - 7)

= (2x² - 7x - 5)(12x - 21)

therefore differentiation of given function is (2x² - 7x - 5)(14x - 21)

also read similar questions : differentiate the following functions w.r.t x . (i)(x^3-2x-1)^5

please mark brainest