Question

if y=(6x-7)^4 find dy/dx​

Answer 1

EXPLANATION.

⇒ y = (6x - 7)⁴.

As we know that,

Differentiate w.r.t x, we get.

⇒ dy/dx = d(6x - 7)⁴/dx.

⇒ dy/dx = 4 x (6x - 7)³ x d(6x)/dx.

⇒ dy/dx = 4 x (6x - 7)³ x (6).

⇒ dy/dx = 24(6x - 7)³.

                                                                                                                           

MORE INFORMATION.

(1) = d(sin x)/dx = cos x.

(2) = d(cos x)/dx = - sin x.

(3) = d(tan x)/dx = sec²x.

(4) = d(cot x)/dx = - cosec²x.

(5) = d(sec x)/dx = sec x tan x.

(6) = d(cosec x)/dx = - cosec x cot x.

(7) = d(constant)/dx = 0.

(8) = d(ax)/dx = a.

(9) = d(xⁿ)/dx = nxⁿ⁻¹.

(10) = d(eˣ)/dx = eˣ.

(11) = d(aˣ)/dx = aˣ㏒a.

(12) = d(㏒x)/dx = 1/x.

Answer 2

★ ANSWER ★

((6*x-7)^4)'

4*(6*x-7)^(4-1)*(6*x-7)'

4*(6*x-7)^(4-1)*((6*x)'+(-7)')

4*(6*x-7)^(4-1)*(6*(x)'+(6)'*x+(-7)')

4*(6*x-7)^(4-1)*(6*(x)'+0*x+(-7)')

4*(6*x-7)^(4-1)*(0*x+6*1+(-7)')

4*(6*x-7)^(4-1)*(0+6)

4*(6*x-7)^(4-1)*6

24*(6*x-7)^3

The calculation above is a derivative of the function f (x).

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