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

The derivative of y=2x(5-3x)^4 is 2((5-3x)^4-12x(5-3x)^3)

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

The first derivative of y=2x(5-3x)^4 is 2((5-3x)^4-12x(5-3x)^3)

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derivative of

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

2 ((5 - 3 x)^{4} - 12 x (5 - 3 x)^{3})

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} ((5 - 3 x)^{4}) = - 12 (5 - 3 x)^{3}

= 2 (1 \cdot (5 - 3 x)^{4} + (- 12 (5 - 3 x)^{3}) x)

Simplify

= 2 ((5 - 3 x)^{4} - 12 x (5 - 3 x)^{3})

x \to 0 lim (\frac{sec ( x )}{x})

x^{2} + 2, 2 x + 5

x^{2} y^{^{''}} + 2 x y^{^{'}} - 12 y = 0

\frac{d}{d x} (cos (e^{t a n (2 x)}))

\int - \frac{1}{2} e^{y} sin (2 y) d y

What is the derivative of y=2x(5-3x)^4 ?
The derivative of y=2x(5-3x)^4 is 2((5-3x)^4-12x(5-3x)^3)
What is the first derivative of y=2x(5-3x)^4 ?
The first derivative of y=2x(5-3x)^4 is 2((5-3x)^4-12x(5-3x)^3)