What is the derivative of (3x^2-5^4(2x^2+1)^3) ?

The derivative of (3x^2-5^4(2x^2+1)^3) is 24x(3x^2-5)^3(2x^2+1)^3+12x(2x^2+1)^2(3x^2-5)^4

What is the first derivative of (3x^2-5^4(2x^2+1)^3) ?

The first derivative of (3x^2-5^4(2x^2+1)^3) is 24x(3x^2-5)^3(2x^2+1)^3+12x(2x^2+1)^2(3x^2-5)^4

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\frac{d}{d x} ((3 x^{2} - 5)^{4} (2 x^{2} + 1)^{3})

24 x (3 x^{2} - 5)^{3} (2 x^{2} + 1)^{3} + 12 x (2 x^{2} + 1)^{2} (3 x^{2} - 5)^{4}

Solution steps

\frac{d}{d x} ((3 x^{2} - 5)^{4} (2 x^{2} + 1)^{3})

Apply the Product Rule:

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

f = (3 x^{2} - 5)^{4}, g = (2 x^{2} + 1)^{3}

= \frac{d}{d x} ((3 x^{2} - 5)^{4}) (2 x^{2} + 1)^{3} + \frac{d}{d x} ((2 x^{2} + 1)^{3}) (3 x^{2} - 5)^{4}

\frac{d}{d x} ((3 x^{2} - 5)^{4}) = 24 x (3 x^{2} - 5)^{3}

\frac{d}{d x} ((2 x^{2} + 1)^{3}) = 12 x (2 x^{2} + 1)^{2}

= 24 x (3 x^{2} - 5)^{3} (2 x^{2} + 1)^{3} + 12 x (2 x^{2} + 1)^{2} (3 x^{2} - 5)^{4}

What is the derivative of (3x^2-5^4(2x^2+1)^3) ?
The derivative of (3x^2-5^4(2x^2+1)^3) is 24x(3x^2-5)^3(2x^2+1)^3+12x(2x^2+1)^2(3x^2-5)^4
What is the first derivative of (3x^2-5^4(2x^2+1)^3) ?
The first derivative of (3x^2-5^4(2x^2+1)^3) is 24x(3x^2-5)^3(2x^2+1)^3+12x(2x^2+1)^2(3x^2-5)^4