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

The derivative of (2x-3^2(5x^2+2)^3) is 4(2x-3)(5x^2+2)^3+30x(5x^2+2)^2(2x-3)^2

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

The first derivative of (2x-3^2(5x^2+2)^3) is 4(2x-3)(5x^2+2)^3+30x(5x^2+2)^2(2x-3)^2

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

4 (2 x - 3) (5 x^{2} + 2)^{3} + 30 x (5 x^{2} + 2)^{2} (2 x - 3)^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} ((5 x^{2} + 2)^{3}) = 30 x (5 x^{2} + 2)^{2}

= 4 (2 x - 3) (5 x^{2} + 2)^{3} + 30 x (5 x^{2} + 2)^{2} (2 x - 3)^{2}

\frac{d}{d x} (- 8 cos (- 4 x - 3))

\frac{1}{s ( s + 2 ) ^{2}}

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

\frac{d ^{2} y}{d x ^{2}} - 10 \frac{d y}{d x} - 3 y = 0

x \to 4 lim ([4 f (8) g (- 1)])

What is the derivative of (2x-3^2(5x^2+2)^3) ?
The derivative of (2x-3^2(5x^2+2)^3) is 4(2x-3)(5x^2+2)^3+30x(5x^2+2)^2(2x-3)^2
What is the first derivative of (2x-3^2(5x^2+2)^3) ?
The first derivative of (2x-3^2(5x^2+2)^3) is 4(2x-3)(5x^2+2)^3+30x(5x^2+2)^2(2x-3)^2