Exercice : Dérivées de fonctions
Calculer les dérivées respectives des fonctions suivantes :
Question
\(f(x)=3x^{2}+5x\)
Solution
\(f'(x)=3\times 2x+5=6x+5\)
Question
\(g(x)=\frac{x^{2}}{8}+9\)
Solution
\(g(x)=\frac{x^{2}}{8}+9\)
\(\iff g(x)=\frac{1}{8}x^{2}+9\)
\(g'(x)=\frac{1}{8}\times 2x\)
\(g'(x)=\frac{1}{4}x\)
Question
\(h(x)=(x+2)(-3x+5)-1\)
Solution
\(h'(x)=(x+2)'(-3x+5)+(x+2)(-3x+5)'\)
\(\iff h'(x)=1(-3x+5)+(x+2)(-3)\)
\(\iff h'(x)=-3x+5-3x-6\)
\(\iff h'(x)=-6x-1\)
Question
\(i(x)\)=\(x^{3}+x^{2}+x+1\)
Solution
\(i'(x)\)=\(3x^{2}+2x+1\)
Question
\(j(x)=3x^{2}-5x+4.\)
Solution
\(j'(x)=3 \times 2x-5\)
\(\iff j'(x)=6x-5\)
Question
\(k(x)=-2x^{3}+3x^{2}+9.\)
Solution
\(k'(x)=-2 \times 3x^{2}+3 \times 2x\)
\(\iff k'(x)=-6x^{2}+6x\)
Question
\(l(x) = x^2 + 2\)
Solution
\(l'(x) = 2x\)
Question
\(m(x) = 2x^2 + 3x − 5\)
Solution
\(m'(x) = 2 \times 2x + 3\)
\(\iff m'(x) = 4x + 3\)
Question
\(n(x) = x^2 + 3x − 1\)
Solution
\(n'(x) = 2x+ 3\)