What is the derivative of y=2t(3t^2-5)^4 ?

The derivative of y=2t(3t^2-5)^4 is 2((3t^2-5)^4+24t^2(3t^2-5)^3)

What is the first derivative of y=2t(3t^2-5)^4 ?

The first derivative of y=2t(3t^2-5)^4 is 2((3t^2-5)^4+24t^2(3t^2-5)^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

y = 2 t (3 t^{2} - 5)^{4}

2 ((3 t^{2} - 5)^{4} + 24 t^{2} (3 t^{2} - 5)^{3})

Solution steps

\frac{d}{d t} (2 t (3 t^{2} - 5)^{4})

Take the constant out:

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

= 2 \frac{d}{d t} (t (3 t^{2} - 5)^{4})

Apply the Product Rule:

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

f = t, g = (3 t^{2} - 5)^{4}

= 2 (\frac{d t}{d t} (3 t^{2} - 5)^{4} + \frac{d}{d t} ((3 t^{2} - 5)^{4}) t)

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

\frac{d}{d t} ((3 t^{2} - 5)^{4}) = 24 t (3 t^{2} - 5)^{3}

= 2 (1 \cdot (3 t^{2} - 5)^{4} + 24 t (3 t^{2} - 5)^{3} t)

Simplify

2 (1 \cdot (3 t^{2} - 5)^{4} + 24 t (3 t^{2} - 5)^{3} t) : 2 ((3 t^{2} - 5)^{4} + 24 t^{2} (3 t^{2} - 5)^{3})

= 2 ((3 t^{2} - 5)^{4} + 24 t^{2} (3 t^{2} - 5)^{3})

\int e^{5 x} cos (9 x) d x

f (x) = \frac{2}{x}, at x = 9

\frac{\partial}{\partial z} (- \frac{1}{( y + 2 z ) ^{2}})

\int \frac{3 e ^{2 x}}{1 + e ^{2 x}} d x

f (x) = sin (2 x), 0, \frac{π}{2}

What is the derivative of y=2t(3t^2-5)^4 ?
The derivative of y=2t(3t^2-5)^4 is 2((3t^2-5)^4+24t^2(3t^2-5)^3)
What is the first derivative of y=2t(3t^2-5)^4 ?
The first derivative of y=2t(3t^2-5)^4 is 2((3t^2-5)^4+24t^2(3t^2-5)^3)