What is the derivative of 100-(200)/(sqrt(t^2+4)) ?

The derivative of 100-(200)/(sqrt(t^2+4)) is (200t)/((t^2+4)^{3/2)}

What is the first derivative of 100-(200)/(sqrt(t^2+4)) ?

The first derivative of 100-(200)/(sqrt(t^2+4)) is (200t)/((t^2+4)^{3/2)}

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derivative of

100 - \frac{200}{t ^{2} + 4}

\frac{200 t}{( t ^{2} + 4 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d t} (100 - \frac{200}{t ^{2} + 4})

Apply the Sum/Difference Rule:

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

= \frac{d}{d t} (100) - \frac{d}{d t} (\frac{200}{t ^{2} + 4})

\frac{d}{d t} (100) = 0

\frac{d}{d t} (\frac{200}{t ^{2} + 4}) = - \frac{200 t}{( t ^{2} + 4 ) ^{\frac{3}{2}}}

= 0 - (- \frac{200 t}{( t ^{2} + 4 ) ^{\frac{3}{2}}})

Simplify

= \frac{200 t}{( t ^{2} + 4 ) ^{\frac{3}{2}}}

What is the derivative of 100-(200)/(sqrt(t^2+4)) ?
The derivative of 100-(200)/(sqrt(t^2+4)) is (200t)/((t^2+4)^{3/2)}
What is the first derivative of 100-(200)/(sqrt(t^2+4)) ?
The first derivative of 100-(200)/(sqrt(t^2+4)) is (200t)/((t^2+4)^{3/2)}