Question

Differentiate:
x^3(sin(5x)^2
Help please

Answer 1

you have to use product rule and chain rule

Answer 2

\[x ^{3} \times \sin(5x)^{2}\]

Answer 3

right?

Answer 4

yes got that bit :)

Answer 5

please stay with me here

Answer 6

thank you :)

Answer 7

lets first find dy/dx of sin(5x)^2

Answer 8

can you work on that?

Answer 9

2sin(5x) * 5?

Answer 10

sorry cos

Answer 11

nooooo wrong

Answer 12

\[dy/dx =\sin(5x)^2= 2\sin(5x)\cos(5x)\]

Answer 13

now find dy/dx of x^3

Answer 14

3x^2

Answer 15

correct

Answer 16

now apply product rule

Answer 17

\[U.dv/dx + V.du/dx\]

Answer 18

let U=x^3
and V=sin(5x)^2

Answer 19

now apply the formular

Answer 20

dv/dx=\[2\sin(5x)\cos(5x)\]

Answer 21

and du/dx=\[3x^2\]

Answer 22

now our result will be

Answer 23

\[2x^3\cos(5x)\sin(5x) + 3x^2\sin(5x)^{2}\]

Answer 24

whic is same as \[x^2(2xcos(5x)\sin(5x)+3\sin(5x)^2)\]

Answer 25

and that is the result

Answer 26

excellent thank you

Answer 27

thanks to openstudy

Answer 28

you didn't differentiate the 5x?

Answer 29

no

Answer 30

ok. did a mistake there

Answer 31

\[dy/dx = [x^3 *(d/dx) (\sin^2(5x))] + [(\sin^2(5x)) * (d/dx) x^3] \]

Answer 32

\[ [x^3 * 2\sin(5x) * (d/dx) \sin(5x)] + [(\sin^2(5x)) * 3x^2] \]

Answer 33

look at this step
\[ [x^3 * 2\sin(5x) * \cos(5x) * (d/dx) 5x] + [(\sin^2(5x)) * 3x^2] \]

Answer 34

\[ [x^3 * 2\sin(5x) * \cos(5x) * 5] + [(\sin^2(5x)) * 3x^2] \]

Answer 35

\[ [10x^3 * \sin(5x) * \cos(5x)] + [3x2 * \sin^2(5x)] \]

Answer 36

thats the result

Answer 37

please close the question

Answer 38

is this

\[\frac{d (x^3\sin(5x)^2)}{dx} = \frac{d (x^3\sin(25x^2))}{dx}\]

or
\[\frac{d (x^3\sin^2(5x))}{dx}\]

looks like the former, has been done as the latter...