What is the derivative of f(t)=sqrt(9t^2-t) ?

The derivative of f(t)=sqrt(9t^2-t) is (18t-1)/(2sqrt(9t^2-t))

What is the first derivative of f(t)=sqrt(9t^2-t) ?

The first derivative of f(t)=sqrt(9t^2-t) is (18t-1)/(2sqrt(9t^2-t))

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derivative of

f (t) = 9 t^{2} - t

\frac{18 t - 1}{2 9 t ^{2} - t}

Solution steps

\frac{d}{d t} (9 t^{2} - t)

Apply the chain rule:

\frac{1}{2 9 t ^{2} - t} \frac{d}{d t} (9 t^{2} - t)

= \frac{1}{2 9 t ^{2} - t} \frac{d}{d t} (9 t^{2} - t)

\frac{d}{d t} (9 t^{2} - t) = 18 t - 1

= \frac{1}{2 9 t ^{2} - t} (18 t - 1)

Simplify

\frac{1}{2 9 t ^{2} - t} (18 t - 1) : \frac{18 t - 1}{2 9 t ^{2} - t}

= \frac{18 t - 1}{2 9 t ^{2} - t}

\int \frac{8 x ^{2}}{9 - x ^{2}} d x

- 2 x^{2} + 3, 0 x

\frac{t ^{2}}{t - 11}

x \to - 4 lim (x^{2} + \frac{2}{x + 4})

\int x 7 - x d x

What is the derivative of f(t)=sqrt(9t^2-t) ?
The derivative of f(t)=sqrt(9t^2-t) is (18t-1)/(2sqrt(9t^2-t))
What is the first derivative of f(t)=sqrt(9t^2-t) ?
The first derivative of f(t)=sqrt(9t^2-t) is (18t-1)/(2sqrt(9t^2-t))