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Math  /  Calculus

QuestionFind the derivatives of these functions: 1. f(x)=x4−5x3+9x2−7x+5f(x)=x^{4}-5 x^{3}+9 x^{2}-7 x+5; 2. g(x)=8x−6x23g(x)=8 \sqrt{x}-\frac{6}{\sqrt[3]{x^{2}}}; 3. h(x)=3x+2x2+1h(x)=\frac{3 x+2}{x^{2}+1}; 4. f(x)=3x(8x−3)7f(x)=3 x(8 x-3)^{7}; 5. f(x)=3x4−4x2+7x−11f(x)=3 x^{4}-4 x^{2}+7 x-11; 6. k(x)=x9−x2k(x)=x \sqrt{9-x^{2}}; 7. f(x)=−3(2x2−5x+1)f(x)=-3(2 x^{2}-5 x+1); 8. g(x)=x23−3x2g(x)=\frac{x^{2}}{3}-\frac{3}{x^{2}}; 9. y=9x2−8x3+2x4y=\frac{9}{x^{2}}-\frac{8}{x^{3}}+\frac{2}{x^{4}}.

Studdy Solution
Find the derivative of the ninth function y=9x2−8x3+2x4y=\frac{9}{x^{2}}-\frac{8}{x^{3}}+\frac{2}{x^{4}}.
y′(x)=−18x−3+24x−4−8x−5y'(x) = -18x^{-3} +24x^{-4} -8x^{-5}

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