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

The derivative of (3^2+5x)^4(2x-2)^3 is 20(9+5x)^3(2x-2)^3+6(2x-2)^2(9+5x)^4

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

The first derivative of (3^2+5x)^4(2x-2)^3 is 20(9+5x)^3(2x-2)^3+6(2x-2)^2(9+5x)^4

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derivative of

(3^{2} + 5 x)^{4} (2 x - 2)^{3}

20 (9 + 5 x)^{3} (2 x - 2)^{3} + 6 (2 x - 2)^{2} (9 + 5 x)^{4}

Solution steps

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

Simplify

(3^{2} + 5 x)^{4} (2 x - 2)^{3} : (9 + 5 x)^{4} (2 x - 2)^{3}

= \frac{d}{d x} ((9 + 5 x)^{4} (2 x - 2)^{3})

Apply the Product Rule:

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

f = (9 + 5 x)^{4}, g = (2 x - 2)^{3}

= \frac{d}{d x} ((9 + 5 x)^{4}) (2 x - 2)^{3} + \frac{d}{d x} ((2 x - 2)^{3}) (9 + 5 x)^{4}

\frac{d}{d x} ((9 + 5 x)^{4}) = 20 (9 + 5 x)^{3}

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

= 20 (9 + 5 x)^{3} (2 x - 2)^{3} + 6 (2 x - 2)^{2} (9 + 5 x)^{4}

\frac{d y}{d x} + y^{3} x + y = 0

d er i v a t i v e - 2 cos (2 x)

d er i v a t i v e f (x) = 2 5^{x}

\int \frac{9}{15 sin ( x ) - 8 cos ( x )} d x

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

What is the derivative of (3^2+5x)^4(2x-2)^3 ?
The derivative of (3^2+5x)^4(2x-2)^3 is 20(9+5x)^3(2x-2)^3+6(2x-2)^2(9+5x)^4
What is the first derivative of (3^2+5x)^4(2x-2)^3 ?
The first derivative of (3^2+5x)^4(2x-2)^3 is 20(9+5x)^3(2x-2)^3+6(2x-2)^2(9+5x)^4