What is the derivative of (4x^3+3^2(5x^2+3)) ?

The derivative of (4x^3+3^2(5x^2+3)) is 640x^7+288x^5+600x^4+216x^2+90x

What is the first derivative of (4x^3+3^2(5x^2+3)) ?

The first derivative of (4x^3+3^2(5x^2+3)) is 640x^7+288x^5+600x^4+216x^2+90x

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\frac{d}{d x} ((4 x^{3} + 3)^{2} (5 x^{2} + 3))

640 x^{7} + 288 x^{5} + 600 x^{4} + 216 x^{2} + 90 x

Solution steps

\frac{d}{d x} ((4 x^{3} + 3)^{2} (5 x^{2} + 3))

Apply the Product Rule:

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

f = (4 x^{3} + 3)^{2}, g = 5 x^{2} + 3

= \frac{d}{d x} ((4 x^{3} + 3)^{2}) (5 x^{2} + 3) + \frac{d}{d x} (5 x^{2} + 3) (4 x^{3} + 3)^{2}

\frac{d}{d x} ((4 x^{3} + 3)^{2}) = 24 x^{2} (4 x^{3} + 3)

\frac{d}{d x} (5 x^{2} + 3) = 10 x

= 24 x^{2} (4 x^{3} + 3) (5 x^{2} + 3) + 10 x (4 x^{3} + 3)^{2}

Simplify

24 x^{2} (4 x^{3} + 3) (5 x^{2} + 3) + 10 x (4 x^{3} + 3)^{2} : 640 x^{7} + 288 x^{5} + 600 x^{4} + 216 x^{2} + 90 x

= 640 x^{7} + 288 x^{5} + 600 x^{4} + 216 x^{2} + 90 x

What is the derivative of (4x^3+3^2(5x^2+3)) ?
The derivative of (4x^3+3^2(5x^2+3)) is 640x^7+288x^5+600x^4+216x^2+90x
What is the first derivative of (4x^3+3^2(5x^2+3)) ?
The first derivative of (4x^3+3^2(5x^2+3)) is 640x^7+288x^5+600x^4+216x^2+90x