Question

differentiate w.r.t x 3/5√(2x^2-7x-5)^5​

Answer 1

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

first resolve the function into simpler form,

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

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

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)

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Answer 2

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