Math  /  Calculus

QuestionFind the derivatives of the following functions:
1. f(x)=x45x3+9x27x+5f(x)=x^{4}-5 x^{3}+9 x^{2}-7 x+5
2. y=3x26xx3y=\frac{3 x^{2}-6 x}{x^{3}}
3. g(x)=8x6x23g(x)=8 \sqrt{x}-\frac{6}{\sqrt[3]{x^{2}}}
4. h(x)=3x+2x2+1h(x)=\frac{3 x+2}{x^{2}+1}
5. f(x)=3x(8x3)7f(x)=3 x(8 x-3)^{7}
6. f(x)=3x44x2+7x11f(x)=3 x^{4}-4 x^{2}+7 x-11
7. k(x)=x9x2k(x)=x \sqrt{9-x^{2}}
8. f(x)=3(2x25x+1)f(x)=-3\left(2 x^{2}-5 x+1\right)
9. g(x)=x233x2g(x)=\frac{x^{2}}{3}-\frac{3}{x^{2}}
10. y=9x28x3+2x4y=\frac{9}{x^{2}}-\frac{8}{x^{3}}+\frac{2}{x^{4}}
11. y=x23x+43y=\sqrt[3]{x^{2}-3 x+4}
12. y=5x25x3xy=5 x^{2}-5 \sqrt{x}-\frac{3}{x}
13. y=x1xy=\sqrt{x}-\frac{1}{\sqrt{x}}
14. y=(3x2)(2x+1)y=(3 x-2)(2 x+1)
15. y=x+1x1y=\frac{\sqrt{x}+1}{\sqrt{x}-1}
16. f(x)=4x33x2+2xf(x)=4 x^{3}-3 x^{2}+2 x
17. y=z5ezlnzy=z^{5}-e^{z} \ln z
18. f(x)=2ex8xf(x)=2 e^{x}-8^{x}

Studdy Solution
Find the derivative of f(x)=2ex8xf(x)=2 e^{x}-8^{x} using the chain rule.
f(x)=2ex8xln8f'(x) =2e^{x} -8^{x} \ln8

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