Question

find the derivative of

Answer 1

hello users ...

solution:-
we know that:
d(u*v)/dx = u * d(v)/dx + v * d(u)/dx 

And
$\frac{d(ax +b)}{dx} = a$
And
$\frac{d( x^{n}) }{dx} = n x^{n-1}$

Here,
d [(x³ - 6x)(2 - 4x³) ] / dx 

 = (x³ - 6x) * d(2 - 4x³) / dx + (2 - 4x³) * d (x³ - 6x) / dx 

= (x³ - 6x) * ( -4 * 3 * x² )  +  (2 - 4x³) * ( 3 * x² - 6 )

= -12x² * (x³ - 6x) + (2 - 4x³) *( 3x² - 6 )

= [tex][-12 x^{5} + 72x^{3} ] + [ 2*( 3x^{2} - 6 ) - 4 x^{3} ( 3 x^{2} - 6 )] [/tex]

= $[-12 x^{5} + 72x^{3} ] + [ 6x^{2} - 12 - 12x^{5} + 24 x^{3} ]$

= $[-12 x^{5} + 72x^{3}  + 6x^{2} - 12 - 12x^{5} + 24 x^{3} ]$

=$[ -24 x^{5} + 96 x^{3} + 6 x^{2} - 12 ]$ Answer

# hope it helps # :)
 

Answer 2

Answer:

- 24 x⁵ + 96 x³ + 6 x² - 12

Step-by-step explanation:

Let say :

y = ( x³ - 6 x ) ( 2 - 4 x³ )

= > y = 2 x³ - 4 x⁶ -  12 x + 24 x⁴

Now :

Diff. w.r.t. :

= > d y / d x = 6 x² - 24 x⁵ - 12 + 96 x³

= > d y / d x =  - 24 x⁵ + 96 x³ + 6 x² - 12

Hence we get required answer! .

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