What is the derivative of 5x^3(2x^2-1) ?

The derivative of 5x^3(2x^2-1) is 5(10x^4-3x^2)

What is the first derivative of 5x^3(2x^2-1) ?

The first derivative of 5x^3(2x^2-1) is 5(10x^4-3x^2)

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\frac{d}{d x} (5 x^{3} (2 x^{2} - 1))

5 (10 x^{4} - 3 x^{2})

Solution steps

\frac{d}{d x} (5 x^{3} (2 x^{2} - 1))

Take the constant out:

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

= 5 \frac{d}{d x} (x^{3} (2 x^{2} - 1))

Apply the Product Rule:

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

f = x^{3}, g = 2 x^{2} - 1

= 5 (\frac{d}{d x} (x^{3}) (2 x^{2} - 1) + \frac{d}{d x} (2 x^{2} - 1) x^{3})

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

\frac{d}{d x} (2 x^{2} - 1) = 4 x

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

Simplify

5 (3 x^{2} (2 x^{2} - 1) + 4 x x^{3}) : 5 (10 x^{4} - 3 x^{2})

= 5 (10 x^{4} - 3 x^{2})

tan (e^{2 t}) + e^{t a n (2 t)}

\frac{1}{1 + 2 x}

x \to 3 lim ((x - 0) \cdot (x - 3))

sin (x), \frac{π}{6}

\int (e^{y^{3} + 2}) d y

What is the derivative of 5x^3(2x^2-1) ?
The derivative of 5x^3(2x^2-1) is 5(10x^4-3x^2)
What is the first derivative of 5x^3(2x^2-1) ?
The first derivative of 5x^3(2x^2-1) is 5(10x^4-3x^2)