What is the derivative of (1+sqrt(t))(8t^2-1) ?

The derivative of (1+sqrt(t))(8t^2-1) is (40t^2+32tsqrt(t)-1)/(2sqrt(t))

What is the first derivative of (1+sqrt(t))(8t^2-1) ?

The first derivative of (1+sqrt(t))(8t^2-1) is (40t^2+32tsqrt(t)-1)/(2sqrt(t))

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derivative of

(1 + t) (8 t^{2} - 1)

\frac{40 t ^{2} + 32 t t - 1}{2 t}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 1 + t, g = 8 t^{2} - 1

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

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

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

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

Simplify

\frac{1}{2 t} (8 t^{2} - 1) + 16 t (1 + t) : \frac{40 t ^{2} + 32 t t - 1}{2 t}

= \frac{40 t ^{2} + 32 t t - 1}{2 t}

x \to \infty lim (3 x^{4})

x \to 0 lim (\frac{e ^{x} - 1}{7 x})

\frac{\partial}{\partial x} (- 5 e^{- 5 y} sin (5 x))

x \to 2 lim (2 - x)

\frac{d}{d t} (\frac{2}{2 - cos ( π t )})

What is the derivative of (1+sqrt(t))(8t^2-1) ?
The derivative of (1+sqrt(t))(8t^2-1) is (40t^2+32tsqrt(t)-1)/(2sqrt(t))
What is the first derivative of (1+sqrt(t))(8t^2-1) ?
The first derivative of (1+sqrt(t))(8t^2-1) is (40t^2+32tsqrt(t)-1)/(2sqrt(t))