Calcular a derivada da função dada
11 set 2017, 01:02
Calcule a derivada da função abaixo:
f(x)= -3(5x³ - 2x + 5).(√x + 2x)
RESPOSTA FINAL: \(f'(x)=-120x^{3}-\frac{105x^{2\sqrt{x}}{}}{2}\ - \frac{15\sqrt{x}}{2x}+9\sqrt{x} \ +24x-30\)
f(x)= -3(5x³ - 2x + 5).(√x + 2x)
RESPOSTA FINAL: \(f'(x)=-120x^{3}-\frac{105x^{2\sqrt{x}}{}}{2}\ - \frac{15\sqrt{x}}{2x}+9\sqrt{x} \ +24x-30\)
Re: Calcular a derivada da função dada [resolvida]
11 set 2017, 17:05
\(f(x)=-3(5x^3-2x+5)(\sqrt{x}+2x)\)
\(f(x)=-3(5x^3.\sqrt{x}+10x^3.x-2x.\sqrt{x}-4x^2+5\sqrt{x}+10x)\)
\(f(x)=-3(5x^{7/2}+10x^4-2x^{3/2}-4x^2+5x^{1/2}+10x)\)
\(f'(x)=-3(5(\frac{7}{2})x^{5/2}+4(10)x^3-2(\frac{3}{2})x^{1/2}-4(2)x+5(\frac{1}{2})x^{-1/2}+10)\)
\(f'(x)=-3(\frac{35}{2}x^{5/2}+40x^3-3x^{1/2}-8x+\frac{5}{2}x^{-1/2}+10)\)
\(f'(x)=-\frac{105}{2}x^2\sqrt{x}-120x^3+9\sqrt{x}+24x-\frac{15}{2\sqrt{x}}-30\)
\(f'(x)=-\frac{105x^2\sqrt{x}}{2}-120x^3+9\sqrt{x}+24x-\frac{15\sqrt{x}}{2x}-30\)
\(f(x)=-3(5x^3.\sqrt{x}+10x^3.x-2x.\sqrt{x}-4x^2+5\sqrt{x}+10x)\)
\(f(x)=-3(5x^{7/2}+10x^4-2x^{3/2}-4x^2+5x^{1/2}+10x)\)
\(f'(x)=-3(5(\frac{7}{2})x^{5/2}+4(10)x^3-2(\frac{3}{2})x^{1/2}-4(2)x+5(\frac{1}{2})x^{-1/2}+10)\)
\(f'(x)=-3(\frac{35}{2}x^{5/2}+40x^3-3x^{1/2}-8x+\frac{5}{2}x^{-1/2}+10)\)
\(f'(x)=-\frac{105}{2}x^2\sqrt{x}-120x^3+9\sqrt{x}+24x-\frac{15}{2\sqrt{x}}-30\)
\(f'(x)=-\frac{105x^2\sqrt{x}}{2}-120x^3+9\sqrt{x}+24x-\frac{15\sqrt{x}}{2x}-30\)