Diketahui f(x) = √(4x² − 6x + 1), maka (dy)/(dx) = …

<p>Jawaban : (dy)/(dx) = (4x - 3)/√(4x² − 6x + 1)</p><p>&nbsp;</p><p>Ingat!</p><p>Jika f(x)=ax^n maka f'(x)=anx^(n-1)&nbsp;</p><p>Jika f(x)=ax maka f'(x)=a</p><p>Jika f(x)=c maka f'(x)=0&nbsp;</p><p>Jika f(x)=(g(x))^n maka f'(x)=n(g(x))^(n-1).g'(x)&nbsp;</p><p>Diketahui fungsi y = f(x), turunannya adalah (dy)/(dx) = f'(x)</p><p>&nbsp;</p><p>Diketahui f(x) = √(4x² − 6x + 1)</p><p>f(x) = (4x² − 6x + 1)^(1/2)</p><p>&nbsp;</p><p>Misalkan f(x) = (g(x))^(1/2) dengan g(x) = 4x² − 6x + 1&nbsp;</p><p>&nbsp;</p><p>Turunan dari g(x) = 4x² − 6x + 1 adalah&nbsp;</p><p>g'(x) = 4.2x - 6 = 8x - 6</p><p>&nbsp;</p><p>Sehingga&nbsp;</p><p>f'(x) = 1/2 (g(x))^(-1/2). g'(x)&nbsp;</p><p>= 1/2 (4x² − 6x + 1)^(-1/2). (8x - 6)&nbsp;</p><p>= (4x - 3) &nbsp;(4x² − 6x + 1)^(-1/2)&nbsp;</p><p>= (4x - 3)/(4x² − 6x + 1)^(1/2)&nbsp;</p><p>= (4x - 3)/√(4x² − 6x + 1)</p><p>&nbsp;</p><p>Misalkan</p><p>y = f(x)</p><p>y = √(4x² − 6x + 1)</p><p>&nbsp;</p><p>turunannya adalah&nbsp;</p><p>(dy)/(dx) = f'(x)</p><p>&nbsp;(dy)/(dx) = (4x - 3)/√(4x² − 6x + 1)</p><p>&nbsp;</p><p>Jadi, (dy)/(dx) = (4x - 3)/√(4x² − 6x + 1)</p>