What is the derivative of 6sqrt(t)-4t^3+9 ?

The derivative of 6sqrt(t)-4t^3+9 is -12t^2+3/(sqrt(t))

What is the first derivative of 6sqrt(t)-4t^3+9 ?

The first derivative of 6sqrt(t)-4t^3+9 is -12t^2+3/(sqrt(t))

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derivative of

6 t - 4 t^{3} + 9

- 12 t^{2} + \frac{3}{t}

Solution steps

\frac{d}{d t} (6 t - 4 t^{3} + 9)

Apply the Sum/Difference Rule:

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

= \frac{d}{d t} (6 t) - \frac{d}{d t} (4 t^{3}) + \frac{d}{d t} (9)

\frac{d}{d t} (6 t) = \frac{3}{t}

\frac{d}{d t} (4 t^{3}) = 12 t^{2}

\frac{d}{d t} (9) = 0

= \frac{3}{t} - 12 t^{2} + 0

Simplify

= - 12 t^{2} + \frac{3}{t}

What is the derivative of 6sqrt(t)-4t^3+9 ?
The derivative of 6sqrt(t)-4t^3+9 is -12t^2+3/(sqrt(t))
What is the first derivative of 6sqrt(t)-4t^3+9 ?
The first derivative of 6sqrt(t)-4t^3+9 is -12t^2+3/(sqrt(t))