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

The derivative of (3x-2)^2(x^4+2)^2 is 90x^9-108x^8+32x^7+216x^5-240x^4+64x^3+72x-48

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

The first derivative of (3x-2)^2(x^4+2)^2 is 90x^9-108x^8+32x^7+216x^5-240x^4+64x^3+72x-48

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derivative of

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

90 x^{9} - 108 x^{8} + 32 x^{7} + 216 x^{5} - 240 x^{4} + 64 x^{3} + 72 x - 48

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} ((3 x - 2)^{2}) = 6 (3 x - 2)

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

= 6 (3 x - 2) (x^{4} + 2)^{2} + 8 x^{3} (x^{4} + 2) (3 x - 2)^{2}

Simplify

6 (3 x - 2) (x^{4} + 2)^{2} + 8 x^{3} (x^{4} + 2) (3 x - 2)^{2} : 90 x^{9} - 108 x^{8} + 32 x^{7} + 216 x^{5} - 240 x^{4} + 64 x^{3} + 72 x - 48

= 90 x^{9} - 108 x^{8} + 32 x^{7} + 216 x^{5} - 240 x^{4} + 64 x^{3} + 72 x - 48

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

\frac{d}{d x} (\frac{6 x}{5 - tan ( x )})

y^{^{''}} - 3 y^{^{'}} + 2 = e^{t}

x \to \infty lim (2 + x)

\int_{0}^{1} \frac{1}{x ln ( x )} d x

What is the derivative of (3x-2)^2(x^4+2)^2 ?
The derivative of (3x-2)^2(x^4+2)^2 is 90x^9-108x^8+32x^7+216x^5-240x^4+64x^3+72x-48
What is the first derivative of (3x-2)^2(x^4+2)^2 ?
The first derivative of (3x-2)^2(x^4+2)^2 is 90x^9-108x^8+32x^7+216x^5-240x^4+64x^3+72x-48