What is the derivative of-6b^2x(a^2-b^2x^2^2) ?

The derivative of-6b^2x(a^2-b^2x^2^2) is -6b^2(5b^4x^4-6b^2a^2x^2+a^4)

What is the first derivative of-6b^2x(a^2-b^2x^2^2) ?

The first derivative of-6b^2x(a^2-b^2x^2^2) is -6b^2(5b^4x^4-6b^2a^2x^2+a^4)

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\frac{d}{d x} (- 6 b^{2} x (a^{2} - b^{2} x^{2})^{2})

- 6 b^{2} (5 b^{4} x^{4} - 6 b^{2} a^{2} x^{2} + a^{4})

Solution steps

\frac{d}{d x} (- 6 b^{2} x (a^{2} - b^{2} x^{2})^{2})

Take the constant out:

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

= - 6 b^{2} \frac{d}{d x} (x (a^{2} - b^{2} x^{2})^{2})

Apply the Product Rule:

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

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

= - 6 b^{2} (\frac{d x}{d x} (a^{2} - b^{2} x^{2})^{2} + \frac{d}{d x} ((a^{2} - b^{2} x^{2})^{2}) x)

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

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

= - 6 b^{2} (1 \cdot (a^{2} - b^{2} x^{2})^{2} + (- 4 b^{2} x (a^{2} - b^{2} x^{2})) x)

Simplify

- 6 b^{2} (1 \cdot (a^{2} - b^{2} x^{2})^{2} + (- 4 b^{2} x (a^{2} - b^{2} x^{2})) x) : - 6 b^{2} (5 b^{4} x^{4} - 6 b^{2} a^{2} x^{2} + a^{4})

= - 6 b^{2} (5 b^{4} x^{4} - 6 b^{2} a^{2} x^{2} + a^{4})

(x + 1)^{3}

t

\int_{0}^{2} \frac{x ^{3}}{x ^{2} + 1} d x

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

\frac{d}{d x} (\frac{x ^{4}}{( 1 + 2 x ) ^{3}})

What is the derivative of-6b^2x(a^2-b^2x^2^2) ?
The derivative of-6b^2x(a^2-b^2x^2^2) is -6b^2(5b^4x^4-6b^2a^2x^2+a^4)
What is the first derivative of-6b^2x(a^2-b^2x^2^2) ?
The first derivative of-6b^2x(a^2-b^2x^2^2) is -6b^2(5b^4x^4-6b^2a^2x^2+a^4)