What is the derivative of 4x^2e^{2x^2+x-1} ?

The derivative of 4x^2e^{2x^2+x-1} is 4(2xe^{2x^2+x-1}+e^{2x^2+x-1}(4x+1)x^2)

What is the first derivative of 4x^2e^{2x^2+x-1} ?

The first derivative of 4x^2e^{2x^2+x-1} is 4(2xe^{2x^2+x-1}+e^{2x^2+x-1}(4x+1)x^2)

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

4 (2 x e^{2 x^{2} + x - 1} + e^{2 x^{2} + x - 1} (4 x + 1) x^{2})

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x^{2}, g = e^{2 x^{2} + x - 1}

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

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

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

= 4 (2 x e^{2 x^{2} + x - 1} + e^{2 x^{2} + x - 1} (4 x + 1) x^{2})

x \to - 3 lim (3 x^{2} + 5 x + 1)

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

\int_{- a}^{a} a^{2} - x^{2} d x

x \to 1 lim (\frac{x ^{2} - 5}{x})

\int y (e^{y}) d y

What is the derivative of 4x^2e^{2x^2+x-1} ?
The derivative of 4x^2e^{2x^2+x-1} is 4(2xe^{2x^2+x-1}+e^{2x^2+x-1}(4x+1)x^2)
What is the first derivative of 4x^2e^{2x^2+x-1} ?
The first derivative of 4x^2e^{2x^2+x-1} is 4(2xe^{2x^2+x-1}+e^{2x^2+x-1}(4x+1)x^2)