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

The derivative of 3x^2(2x+1^5) is 3(2x(2x+1)^5+10(2x+1)^4x^2)

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

The first derivative of 3x^2(2x+1^5) is 3(2x(2x+1)^5+10(2x+1)^4x^2)

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

3 (2 x (2 x + 1)^{5} + 10 (2 x + 1)^{4} x^{2})

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} ((2 x + 1)^{5}) = 10 (2 x + 1)^{4}

= 3 (2 x (2 x + 1)^{5} + 10 (2 x + 1)^{4} x^{2})

What is the derivative of 3x^2(2x+1^5) ?
The derivative of 3x^2(2x+1^5) is 3(2x(2x+1)^5+10(2x+1)^4x^2)
What is the first derivative of 3x^2(2x+1^5) ?
The first derivative of 3x^2(2x+1^5) is 3(2x(2x+1)^5+10(2x+1)^4x^2)