What is the derivative of f(t)=sqrt(4t^2-t) ?

The derivative of f(t)=sqrt(4t^2-t) is (8t-1)/(2sqrt(4t^2-t))

What is the first derivative of f(t)=sqrt(4t^2-t) ?

The first derivative of f(t)=sqrt(4t^2-t) is (8t-1)/(2sqrt(4t^2-t))

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derivative of

f (t) = 4 t^{2} - t

\frac{8 t - 1}{2 4 t ^{2} - t}

Solution steps

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

Apply the chain rule:

\frac{1}{2 4 t ^{2} - t} \frac{d}{d t} (4 t^{2} - t)

= \frac{1}{2 4 t ^{2} - t} \frac{d}{d t} (4 t^{2} - t)

\frac{d}{d t} (4 t^{2} - t) = 8 t - 1

= \frac{1}{2 4 t ^{2} - t} (8 t - 1)

Simplify

\frac{1}{2 4 t ^{2} - t} (8 t - 1) : \frac{8 t - 1}{2 4 t ^{2} - t}

= \frac{8 t - 1}{2 4 t ^{2} - t}

What is the derivative of f(t)=sqrt(4t^2-t) ?
The derivative of f(t)=sqrt(4t^2-t) is (8t-1)/(2sqrt(4t^2-t))
What is the first derivative of f(t)=sqrt(4t^2-t) ?
The first derivative of f(t)=sqrt(4t^2-t) is (8t-1)/(2sqrt(4t^2-t))