Jawaban:
1a.
rumus: y = f(g(x)) => y' = f'(g(x)) × g'(x)
[tex] \frac{dy}{dx} = 7( {x}^{3} - 5 {x}^{2} + 6) ^{7 - 1} \times (3 {x}^{3 - 1} - 5(2) {x}^{2 - 1} )[/tex]
[tex] = 7( {x}^{3} - 5 {x}^{2} + 6) ^{6} (3 {x}^{2} - 10x)[/tex]
b.
rumus: y = u•v => y' = u'v + uv'
mis u = x²-5
u' = 2x
v = (4x+5)^6
v' = 6(4x+5)^5 × 4
= 24(4x+5)^5
[tex] \frac{dy}{dx} = 2x(4x + 5)^{6} + ( {x}^{2} - 5) \times 24(4x + 5) ^{5} [/tex]
[tex] = 2x(4x + 5)^{6} + 24( {x}^{2} - 5)(4x + 5) ^{5} [/tex]
c.
rumus: y = u/v => y' = (u'v - uv') / v²
mis u = (x-6)(x+3)^6
u' = (x+3)^6 + 6(x+6)(x+3)^5
= (x+3)^5 × (x+3 + 6(x+6))
= (7x+39)(x+3)^5
v = 3x
v' = 3
[tex] \frac{dy}{dx} = \frac{(7x + 39) {(x + 3)}^{5} - 3(x - 6) {(x + 3)}^{6} }{ {3}^{2} } [/tex]
[tex]= \frac{{(x + 3)}^{5} (7x + 39 - 3(x - 6) (x + 3))}{ 9 } [/tex]
[tex]= \frac{{(x + 3)}^{5} (7x + 39 - 3 {x}^{2} + 9x + 54 )}{ 9 } [/tex]
[tex]= \frac{{(x + 3)}^{5} ( - 3 {x}^{2} + 16x + 93 )}{ 9 } [/tex]
2.
[tex]f(x) = {x}^{ \frac{1}{2} } - 6 {x}^{ - 3} + 5 {x}^{2} + 7x[/tex]
[tex] \frac{dy}{dx} = \frac{1}{2} {x}^{ - \frac{1}{2} } + 18{x}^{ - 4} + 10x [/tex]
[tex]\frac{d^{2} y}{d {x}^{2} } = - \frac{1}{4} {x}^{ - \frac{3}{2} } - 72{x}^{ - 5} + 10 [/tex]
Jawaban:
1x1x1x1x1x1x1x1
Penjelasan dengan langkah-langkah:
samadengan 2
