What is the derivative of-5t(3t^8-1)^7 ?

The derivative of-5t(3t^8-1)^7 is -5((3t^8-1)^7+168t^8(3t^8-1)^6)

What is the first derivative of-5t(3t^8-1)^7 ?

The first derivative of-5t(3t^8-1)^7 is -5((3t^8-1)^7+168t^8(3t^8-1)^6)

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derivative of

- 5 t (3 t^{8} - 1)^{7}

- 5 ((3 t^{8} - 1)^{7} + 168 t^{8} (3 t^{8} - 1)^{6})

Solution steps

\frac{d}{d t} (- 5 t (3 t^{8} - 1)^{7})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - 5 \frac{d}{d t} (t (3 t^{8} - 1)^{7})

Apply the Product Rule:

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

f = t, g = (3 t^{8} - 1)^{7}

= - 5 (\frac{d t}{d t} (3 t^{8} - 1)^{7} + \frac{d}{d t} ((3 t^{8} - 1)^{7}) t)

\frac{d t}{d t} = 1

\frac{d}{d t} ((3 t^{8} - 1)^{7}) = 168 t^{7} (3 t^{8} - 1)^{6}

= - 5 (1 \cdot (3 t^{8} - 1)^{7} + 168 t^{7} (3 t^{8} - 1)^{6} t)

Simplify

- 5 (1 \cdot (3 t^{8} - 1)^{7} + 168 t^{7} (3 t^{8} - 1)^{6} t) : - 5 ((3 t^{8} - 1)^{7} + 168 t^{8} (3 t^{8} - 1)^{6})

= - 5 ((3 t^{8} - 1)^{7} + 168 t^{8} (3 t^{8} - 1)^{6})

\frac{d}{d x} (\frac{3 x ^{2} + 5 x}{x})

\frac{d s}{\frac{d t}{2}} = s

\frac{d ^{10}}{d x ^{10}} (cos (2 x))

t^{2} \cdot \frac{d x}{d t} = \frac{1}{x}

\frac{d}{d x} (8 x e^{4 x})

What is the derivative of-5t(3t^8-1)^7 ?
The derivative of-5t(3t^8-1)^7 is -5((3t^8-1)^7+168t^8(3t^8-1)^6)
What is the first derivative of-5t(3t^8-1)^7 ?
The first derivative of-5t(3t^8-1)^7 is -5((3t^8-1)^7+168t^8(3t^8-1)^6)