What is the derivative of y=sqrt(1/(t(8t+1))) ?

The derivative of y=sqrt(1/(t(8t+1))) is 1/(2sqrt((1){t(8t+1))}}(-\frac{16t+1)/(t^2(8t+1)^2))

What is the first derivative of y=sqrt(1/(t(8t+1))) ?

The first derivative of y=sqrt(1/(t(8t+1))) is 1/(2sqrt((1){t(8t+1))}}(-\frac{16t+1)/(t^2(8t+1)^2))

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derivative of

y = \frac{1}{t ( 8 t + 1 )}

\frac{1}{2 \frac{1}{t ( 8 t + 1 )}} (- \frac{16 t + 1}{t ^{2} ( 8 t + 1 ) ^{2}})

Solution steps

\frac{d}{d t} (\frac{1}{t ( 8 t + 1 )})

Apply the chain rule:

\frac{1}{2 \frac{1}{t ( 8 t + 1 )}} \frac{d}{d t} (\frac{1}{t ( 8 t + 1 )})

= \frac{1}{2 \frac{1}{t ( 8 t + 1 )}} \frac{d}{d t} (\frac{1}{t ( 8 t + 1 )})

\frac{d}{d t} (\frac{1}{t ( 8 t + 1 )}) = - \frac{16 t + 1}{t ^{2} ( 8 t + 1 ) ^{2}}

= \frac{1}{2 \frac{1}{t ( 8 t + 1 )}} (- \frac{16 t + 1}{t ^{2} ( 8 t + 1 ) ^{2}})

What is the derivative of y=sqrt(1/(t(8t+1))) ?
The derivative of y=sqrt(1/(t(8t+1))) is 1/(2sqrt((1){t(8t+1))}}(-\frac{16t+1)/(t^2(8t+1)^2))
What is the first derivative of y=sqrt(1/(t(8t+1))) ?
The first derivative of y=sqrt(1/(t(8t+1))) is 1/(2sqrt((1){t(8t+1))}}(-\frac{16t+1)/(t^2(8t+1)^2))