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

The derivative of f(x)=(2x^2-1)^2(3x^2) is 3(24x^5-16x^3+2x)

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

The first derivative of f(x)=(2x^2-1)^2(3x^2) is 3(24x^5-16x^3+2x)

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derivative of

f (x) = (2 x^{2} - 1)^{2} (3 x^{2})

3 (24 x^{5} - 16 x^{3} + 2 x)

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = (2 x^{2} - 1)^{2}, g = x^{2}

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

\frac{d}{d x} ((2 x^{2} - 1)^{2}) = 8 x (2 x^{2} - 1)

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

= 3 (8 x (2 x^{2} - 1) x^{2} + 2 x (2 x^{2} - 1)^{2})

Simplify

3 (8 x (2 x^{2} - 1) x^{2} + 2 x (2 x^{2} - 1)^{2}) : 3 (24 x^{5} - 16 x^{3} + 2 x)

= 3 (24 x^{5} - 16 x^{3} + 2 x)

e^{2 x}

2 sin (θ)

\frac{\partial}{\partial x} (x^{2} + 2 x y + 2 y^{2} - 8 x + 8 y)

\int_{1}^{\infty} \frac{1}{x ^{2} + 3} d x

y = 3 1.6 x^{2} + 4.9

What is the derivative of f(x)=(2x^2-1)^2(3x^2) ?
The derivative of f(x)=(2x^2-1)^2(3x^2) is 3(24x^5-16x^3+2x)
What is the first derivative of f(x)=(2x^2-1)^2(3x^2) ?
The first derivative of f(x)=(2x^2-1)^2(3x^2) is 3(24x^5-16x^3+2x)