Y = arcsin( 2x4+5x3) carilah y'
Matematika
tryulianii
Pertanyaan
Y = arcsin( 2x4+5x3) carilah y'
1 Jawaban
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1. Jawaban nabnabs
[tex]y=\arcsin{2x^{4}+5x^{3}}[/tex]
[tex]\sin{y}=2x^{4}+5x^{3}[/tex]
[tex]\cos{y} \frac{dy}{dx}=8x^{3}+15x^{2}[/tex]
[tex]\frac{dy}{dx}=\frac{8x^{3}+15x^{2}}{\cos{y}}[/tex]
perhatikan bahwa
[tex]\cos{y}=\sqrt{1-\sin^{2}{y}}[/tex]
[tex]\frac{dy}{dx}=\frac{8x^{3}+15x^{2}}{{\sqrt{1-\sin^{2}{y}}}}[/tex]
[tex]=\frac{8x^{3}+15x^{2}}{\sqrt{1-(2x^{4}+5x^{3})^{2}}}[/tex]