What is the derivative of (2-x^2(4x^2+9x)^4) ?

The derivative of (2-x^2(4x^2+9x)^4) is -2x(4x^2+9x)^4+4(4x^2+9x)^3(8x+9)(2-x^2)

What is the first derivative of (2-x^2(4x^2+9x)^4) ?

The first derivative of (2-x^2(4x^2+9x)^4) is -2x(4x^2+9x)^4+4(4x^2+9x)^3(8x+9)(2-x^2)

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\frac{d}{d x} ((2 - x^{2}) (4 x^{2} + 9 x)^{4})

- 2 x (4 x^{2} + 9 x)^{4} + 4 (4 x^{2} + 9 x)^{3} (8 x + 9) (2 - x^{2})

Solution steps

\frac{d}{d x} ((2 - x^{2}) (4 x^{2} + 9 x)^{4})

Apply the Product Rule:

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

f = 2 - x^{2}, g = (4 x^{2} + 9 x)^{4}

= \frac{d}{d x} (2 - x^{2}) (4 x^{2} + 9 x)^{4} + \frac{d}{d x} ((4 x^{2} + 9 x)^{4}) (2 - x^{2})

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

\frac{d}{d x} ((4 x^{2} + 9 x)^{4}) = 4 (4 x^{2} + 9 x)^{3} (8 x + 9)

= (- 2 x) (4 x^{2} + 9 x)^{4} + 4 (4 x^{2} + 9 x)^{3} (8 x + 9) (2 - x^{2})

Simplify

= - 2 x (4 x^{2} + 9 x)^{4} + 4 (4 x^{2} + 9 x)^{3} (8 x + 9) (2 - x^{2})

\frac{d}{d x} (\frac{5 ^{x}}{x ^{5}})

\int (x^{4} + x^{2} + x) d x

\frac{\partial}{\partial x} (x^{8})

y = \frac{1}{2 + 3 x}, (2, \frac{1}{8})

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

What is the derivative of (2-x^2(4x^2+9x)^4) ?
The derivative of (2-x^2(4x^2+9x)^4) is -2x(4x^2+9x)^4+4(4x^2+9x)^3(8x+9)(2-x^2)
What is the first derivative of (2-x^2(4x^2+9x)^4) ?
The first derivative of (2-x^2(4x^2+9x)^4) is -2x(4x^2+9x)^4+4(4x^2+9x)^3(8x+9)(2-x^2)