What is the derivative of 4x^2*2^{(3x+1}) ?

The derivative of 4x^2*2^{(3x+1}) is 3ln(2)*2^{3x+3}x^2+2^{3x+4}x

What is the first derivative of 4x^2*2^{(3x+1}) ?

The first derivative of 4x^2*2^{(3x+1}) is 3ln(2)*2^{3x+3}x^2+2^{3x+4}x

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

3 ln (2) \cdot 2^{3 x + 3} x^{2} + 2^{3 x + 4} x

Solution steps

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

Simplify

4 x^{2} \cdot 2^{(3 x + 1)} : 2^{3 x + 3} x^{2}

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

Apply the Product Rule:

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

f = 2^{3 x + 3}, g = x^{2}

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

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

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

= 3 ln (2) \cdot 2^{3 x + 3} x^{2} + 2 x \cdot 2^{3 x + 3}

2 x \cdot 2^{3 x + 3} = 2^{3 x + 4} x

= 3 ln (2) \cdot 2^{3 x + 3} x^{2} + 2^{3 x + 4} x

\frac{\partial}{\partial x} ((x^{2} + y^{2}) e^{y^{2} - x^{2}})

\int 2 - x d x

x \to 3 + lim (4)

What is the derivative of 4x^2*2^{(3x+1}) ?
The derivative of 4x^2*2^{(3x+1}) is 3ln(2)*2^{3x+3}x^2+2^{3x+4}x
What is the first derivative of 4x^2*2^{(3x+1}) ?
The first derivative of 4x^2*2^{(3x+1}) is 3ln(2)*2^{3x+3}x^2+2^{3x+4}x