What is the derivative of 72x(6x^2+8^5) ?

The derivative of 72x(6x^2+8^5) is 72((6x^2+8)^5+60x^2(6x^2+8)^4)

What is the first derivative of 72x(6x^2+8^5) ?

The first derivative of 72x(6x^2+8^5) is 72((6x^2+8)^5+60x^2(6x^2+8)^4)

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\frac{d}{d x} (72 x (6 x^{2} + 8)^{5})

72 ((6 x^{2} + 8)^{5} + 60 x^{2} (6 x^{2} + 8)^{4})

Solution steps

\frac{d}{d x} (72 x (6 x^{2} + 8)^{5})

Take the constant out:

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

= 72 \frac{d}{d x} (x (6 x^{2} + 8)^{5})

Apply the Product Rule:

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

f = x, g = (6 x^{2} + 8)^{5}

= 72 (\frac{d x}{d x} (6 x^{2} + 8)^{5} + \frac{d}{d x} ((6 x^{2} + 8)^{5}) x)

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

\frac{d}{d x} ((6 x^{2} + 8)^{5}) = 60 x (6 x^{2} + 8)^{4}

= 72 (1 \cdot (6 x^{2} + 8)^{5} + 60 x (6 x^{2} + 8)^{4} x)

Simplify

72 (1 \cdot (6 x^{2} + 8)^{5} + 60 x (6 x^{2} + 8)^{4} x) : 72 ((6 x^{2} + 8)^{5} + 60 x^{2} (6 x^{2} + 8)^{4})

= 72 ((6 x^{2} + 8)^{5} + 60 x^{2} (6 x^{2} + 8)^{4})

\frac{d}{d x} (\frac{5 x - 2}{x ^{2} + 1})

x \to 0 - lim (\frac{x - 59}{x})

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

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

\frac{\partial}{\partial y} (y - e^{t})

What is the derivative of 72x(6x^2+8^5) ?
The derivative of 72x(6x^2+8^5) is 72((6x^2+8)^5+60x^2(6x^2+8)^4)
What is the first derivative of 72x(6x^2+8^5) ?
The first derivative of 72x(6x^2+8^5) is 72((6x^2+8)^5+60x^2(6x^2+8)^4)