What is the derivative of f(x)=20x^{1/2}-1/2 x^{20} ?

The derivative of f(x)=20x^{1/2}-1/2 x^{20} is (10-10x^{39/2})/(x^{1/2)}

What is the first derivative of f(x)=20x^{1/2}-1/2 x^{20} ?

The first derivative of f(x)=20x^{1/2}-1/2 x^{20} is (10-10x^{39/2})/(x^{1/2)}

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derivative of

f (x) = 20 x^{\frac{1}{2}} - \frac{1}{2} x^{20}

\frac{10 - 10 x ^{\frac{39}{2}}}{x ^{\frac{1}{2}}}

Solution steps

\frac{d}{d x} (20 x^{\frac{1}{2}} - \frac{1}{2} x^{20})

Simplify

20 x^{\frac{1}{2}} - \frac{1}{2} x^{20} : 20 x^{\frac{1}{2}} - \frac{x ^{20}}{2}

= \frac{d}{d x} (20 x^{\frac{1}{2}} - \frac{x ^{20}}{2})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (20 x^{\frac{1}{2}}) - \frac{d}{d x} (\frac{x ^{20}}{2})

\frac{d}{d x} (20 x^{\frac{1}{2}}) = \frac{10}{x ^{\frac{1}{2}}}

\frac{d}{d x} (\frac{x ^{20}}{2}) = 10 x^{19}

= \frac{10}{x ^{\frac{1}{2}}} - 10 x^{19}

Simplify

\frac{10}{x ^{\frac{1}{2}}} - 10 x^{19} : \frac{10 - 10 x ^{\frac{39}{2}}}{x ^{\frac{1}{2}}}

= \frac{10 - 10 x ^{\frac{39}{2}}}{x ^{\frac{1}{2}}}

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\int \frac{2 x ^{3} - 4 x ^{2} - 9 x - 1}{x ^{2} - 2 x - 5} d x

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What is the derivative of f(x)=20x^{1/2}-1/2 x^{20} ?
The derivative of f(x)=20x^{1/2}-1/2 x^{20} is (10-10x^{39/2})/(x^{1/2)}
What is the first derivative of f(x)=20x^{1/2}-1/2 x^{20} ?
The first derivative of f(x)=20x^{1/2}-1/2 x^{20} is (10-10x^{39/2})/(x^{1/2)}