What is the derivative of (x^2-8(5x^3)) ?

The derivative of (x^2-8(5x^3)) is 5(5x^4-24x^2)

What is the first derivative of (x^2-8(5x^3)) ?

The first derivative of (x^2-8(5x^3)) is 5(5x^4-24x^2)

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\frac{d}{d x} ((x^{2} - 8) (5 x^{3}))

5 (5 x^{4} - 24 x^{2})

Solution steps

\frac{d}{d x} ((x^{2} - 8) (5 x^{3}))

Take the constant out:

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

= 5 \frac{d}{d x} ((x^{2} - 8) x^{3})

Apply the Product Rule:

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

f = x^{2} - 8, g = x^{3}

= 5 (\frac{d}{d x} (x^{2} - 8) x^{3} + \frac{d}{d x} (x^{3}) (x^{2} - 8))

\frac{d}{d x} (x^{2} - 8) = 2 x

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

= 5 (2 x x^{3} + 3 x^{2} (x^{2} - 8))

Simplify

5 (2 x x^{3} + 3 x^{2} (x^{2} - 8)) : 5 (5 x^{4} - 24 x^{2})

= 5 (5 x^{4} - 24 x^{2})

\int \frac{cos ( ln ( 2 x ) )}{x} d x

\int \frac{x ^{2} + 16 x - 4}{x ^{3} - 4 x} d x

y = \frac{1}{3 + 2 x}, (2, \frac{1}{7})

7 x - 6 y x^{2} + 1 \frac{d y}{d x} = 0

\frac{d y}{d x} = (e^{4 x + 3 y})

What is the derivative of (x^2-8(5x^3)) ?
The derivative of (x^2-8(5x^3)) is 5(5x^4-24x^2)
What is the first derivative of (x^2-8(5x^3)) ?
The first derivative of (x^2-8(5x^3)) is 5(5x^4-24x^2)