Question

Ache a derivada f´(x) das seguintes funções:


a)F(s) = s∧3 + 2s∧2 – s + 1

Answer 1

• $\dfrac{d}{dy}(cx^n)=n.c.x^{n-1}$

• $\dfrac{d}{dy}\:(c)=0$

$F(s)=s^3+2s^2-s+1\\\\F(x)=3s^{3-1}+2.2s^{2-1}-1s^{1-1}+0\\\\F'(s)=3s^2+4s-1$

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$f(x)=7x^3-2x^2+x-1\\\\f'(x)7.3x^{3-1}-2.2x^{2-1}+1.x^{1-1}-0\\\\f'(x)=21x^2-4x+1$

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$g(x)=-\frac{1}{4}x^4+\frac{2}{3}x^3-\frac{1}{2}x^2+\frac{1}{4}\\\\g'(x)=-\frac{1.4}{4}x^{4-1}+\frac{2.3}{3}x^{3-1}-\frac{1.2}{2}x^{2-1}+0\\\\g'(x)=-x^3+2x^2-x$