What is the derivative of (x^2+4^2(2x^3-1)^3) ?

The derivative of (x^2+4^2(2x^3-1)^3) is 4x(x^2+4)(2x^3-1)^3+18x^2(2x^3-1)^2(x^2+4)^2

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

The first derivative of (x^2+4^2(2x^3-1)^3) is 4x(x^2+4)(2x^3-1)^3+18x^2(2x^3-1)^2(x^2+4)^2

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

4 x (x^{2} + 4) (2 x^{3} - 1)^{3} + 18 x^{2} (2 x^{3} - 1)^{2} (x^{2} + 4)^{2}

Solution steps

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

Apply the Product Rule:

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

f = (x^{2} + 4)^{2}, g = (2 x^{3} - 1)^{3}

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

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

\frac{d}{d x} ((2 x^{3} - 1)^{3}) = 18 x^{2} (2 x^{3} - 1)^{2}

= 4 x (x^{2} + 4) (2 x^{3} - 1)^{3} + 18 x^{2} (2 x^{3} - 1)^{2} (x^{2} + 4)^{2}

f (x) = \frac{2}{1 + e ^{- x}}

\int 7 sin^{5} (x) cos^{- \frac{3}{2}} (x) d x

\int_{0}^{2} \int_{0}^{3} (\frac{x ^{2} y ^{2}}{4}) d x d y

f (x) = sin (5 ln (x))

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

What is the derivative of (x^2+4^2(2x^3-1)^3) ?
The derivative of (x^2+4^2(2x^3-1)^3) is 4x(x^2+4)(2x^3-1)^3+18x^2(2x^3-1)^2(x^2+4)^2
What is the first derivative of (x^2+4^2(2x^3-1)^3) ?
The first derivative of (x^2+4^2(2x^3-1)^3) is 4x(x^2+4)(2x^3-1)^3+18x^2(2x^3-1)^2(x^2+4)^2