What is the derivative of-4t(3t^5-1)^4 ?

The derivative of-4t(3t^5-1)^4 is -4((3t^5-1)^4+60t^5(3t^5-1)^3)

What is the first derivative of-4t(3t^5-1)^4 ?

The first derivative of-4t(3t^5-1)^4 is -4((3t^5-1)^4+60t^5(3t^5-1)^3)

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derivative of

- 4 t (3 t^{5} - 1)^{4}

- 4 ((3 t^{5} - 1)^{4} + 60 t^{5} (3 t^{5} - 1)^{3})

Solution steps

\frac{d}{d t} (- 4 t (3 t^{5} - 1)^{4})

Take the constant out:

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

= - 4 \frac{d}{d t} (t (3 t^{5} - 1)^{4})

Apply the Product Rule:

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

f = t, g = (3 t^{5} - 1)^{4}

= - 4 (\frac{d t}{d t} (3 t^{5} - 1)^{4} + \frac{d}{d t} ((3 t^{5} - 1)^{4}) t)

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

\frac{d}{d t} ((3 t^{5} - 1)^{4}) = 60 t^{4} (3 t^{5} - 1)^{3}

= - 4 (1 \cdot (3 t^{5} - 1)^{4} + 60 t^{4} (3 t^{5} - 1)^{3} t)

Simplify

- 4 (1 \cdot (3 t^{5} - 1)^{4} + 60 t^{4} (3 t^{5} - 1)^{3} t) : - 4 ((3 t^{5} - 1)^{4} + 60 t^{5} (3 t^{5} - 1)^{3})

= - 4 ((3 t^{5} - 1)^{4} + 60 t^{5} (3 t^{5} - 1)^{3})

\frac{d}{d x} (ln (x x^{2} - 10))

f (x) = 4 x^{2} - 3 x + 2

\int_{0}^{5} x^{2} d x

\frac{d}{d x} (y^{1 - n})

\int - \frac{x ^{3}}{3 e ^{\frac{x}{2}}} d x

What is the derivative of-4t(3t^5-1)^4 ?
The derivative of-4t(3t^5-1)^4 is -4((3t^5-1)^4+60t^5(3t^5-1)^3)
What is the first derivative of-4t(3t^5-1)^4 ?
The first derivative of-4t(3t^5-1)^4 is -4((3t^5-1)^4+60t^5(3t^5-1)^3)