Question

QUIZ (1422)
Materi: Fungsi

Tentukan derivatif dari [tex] f(x)=7x^3 + 5x^2 +9x [/tex] !​

Answer 1

Verified answer

Turunan Fungsi Aljabar

[Derivatif]

..

[tex]\begin{gathered}\boxed{\begin{array}{lll}f(x)=k~;~k=konstanta\Longrightarrow f'(x)=0\\\\f(x)=ax^n~\Longrightarrow f'(x)=n.ax^{n-1}\\\\f(x)=k\times g(x)\Longrightarrow f'(x)=k\times g'(x)\\\\f(x)=(ax^m+k)^n\Longrightarrow f'(x)=n\times ax^{m-1}(ax^m+k)^{n-1}\\\\f(x)=g(x)\pm h(x)\Longrightarrow f'(x)=g'(x)\pm h'(x)\\\\f(x)=g(x)\times h(x)\Longrightarrow f'(x)=g'(x)\times h(x)+ g(x)\times h'(x)\\\\f(x)=\dfrac{g(x)}{h(x)}\Longrightarrow f'(x)=\dfrac{g'(x)\times h(x)-g(x)\times h'(x)}{(h(x))^2}\end{array}}\end{gathered}[/tex]

Penyelesaian Soal

[tex]\begin{aligned} f(x) &=7x^3 + 5x^2 +9x \\ \\ f'(x) &= 7 \times 3x^{3 - 2} + 5 \times 2x^{2 - 1} + 9 \\&= 7 \times 3x^2 + 5 \times 2x + 9 \\&= \boxed{\bold{\underline{21x^2 + 10x + 9}}} \end{aligned}[/tex]

[tex]\begin{array}{lr}\texttt{}\end{array}[/tex]

[tex]\boxed{\colorbox{ccddff}{Answered by Danial Alf'at | 09 - 05 - 2023}}[/tex]

Answer 2

Jawaban:

derivatif

f'(x) = 21x² + 10x + 9

Penjelasan dengan langkah-langkah:

Rumus derivatif

[tex] \boxed{ \large a {x}^{n} = n.a {x}^{n - 1} }[/tex]

---

f(x) = 7x³ + 5x² + 9x [tex] \rm f'(x) = 7.3 {x}^{3 - 1} + 5.2 {x}^{2 - 1} + 9 {x}^{1 - 1} [/tex]

[tex]f'(x) = 21 {x}^{2} + 10x + 9[/tex]