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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

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