Question

How to differentiate this​

Answer 1

Step-by-step explanation:

check it.. i have solved this for you

Answer 2

Answer:

18

Step-by-step explanation:

Using the product rule

Given

y = f(x). g(x) , then

$\frac{dy}{dx}$ = f(x). g'(x) + g(x). f'(x)

Here

f(x) = $(2x+3)^{5}$ ⇒ f'(x) = 5$(2x+3)^{4}$ × $\frac{d}{dx}$ (2x + 3) , then

f'(x) = 10$(2x+3)^{4}$

g(x) = $(x+2)^{8}$ ⇒ g'(x) = 8$(x+2)^{7}$ × $\frac{d}{dx}$ (x + 2) , then

g'(x) = 8$(x+2)^{7}$

Thus

$\frac{dy}{dx}$ = $(2x+3)^{5}$ . 8$(x+2)^{7}$ + $(x+2)^{8}$ . 10$(2x+3)^{4}$ ← factor expression

    = $(2x+3)^{4}$ $(x+2)^{7}$ [ 8(2x + 3) + 10(x + 2)

    = $(2x+3)^{4}$ $(x+2)^{7}$ (16x + 24 + 10x + 20)

    = $(2x+3)^{4}$ $(x+2)^{7}$ (26x + 44)

Thus

$\frac{dy}{dx}$ ( x = - 1)

= $1^{4}$ × $1^{7}$ × 18

= 1 × 1 × 18

= 18