What is the derivative of 6(4e^{x^2}x^3+6e^{x^2}x) ?

The derivative of 6(4e^{x^2}x^3+6e^{x^2}x) is 6(8e^{x^2}x^4+24e^{x^2}x^2+6e^{x^2})

What is the first derivative of 6(4e^{x^2}x^3+6e^{x^2}x) ?

The first derivative of 6(4e^{x^2}x^3+6e^{x^2}x) is 6(8e^{x^2}x^4+24e^{x^2}x^2+6e^{x^2})

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\frac{d}{d x} (6 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x))

6 (8 e^{x^{2}} x^{4} + 24 e^{x^{2}} x^{2} + 6 e^{x^{2}})

Solution steps

\frac{d}{d x} (6 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x))

Take the constant out:

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

= 6 \frac{d}{d x} (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 6 (\frac{d}{d x} (4 e^{x^{2}} x^{3}) + \frac{d}{d x} (6 e^{x^{2}} x))

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

\frac{d}{d x} (6 e^{x^{2}} x) = 6 (2 e^{x^{2}} x^{2} + e^{x^{2}})

= 6 (4 (2 e^{x^{2}} x^{4} + 3 e^{x^{2}} x^{2}) + 6 (2 e^{x^{2}} x^{2} + e^{x^{2}}))

Expand

4 (2 e^{x^{2}} x^{4} + 3 e^{x^{2}} x^{2}) + 6 (2 e^{x^{2}} x^{2} + e^{x^{2}}) : 8 e^{x^{2}} x^{4} + 24 e^{x^{2}} x^{2} + 6 e^{x^{2}}

= 6 (8 e^{x^{2}} x^{4} + 24 e^{x^{2}} x^{2} + 6 e^{x^{2}})

5 x^{^{''}} + 5 x^{^{'}} + 6 x = 0, x^{^{'}} (0) = 0.45, x (0) = - 0.3

\int \frac{cos ( x )}{x} d x

\frac{\partial}{\partial x} (x z^{2})

\int \frac{5}{6 + 5 x} d x

\int \frac{1 - x ^{2}}{x ^{4}} d x

What is the derivative of 6(4e^{x^2}x^3+6e^{x^2}x) ?
The derivative of 6(4e^{x^2}x^3+6e^{x^2}x) is 6(8e^{x^2}x^4+24e^{x^2}x^2+6e^{x^2})
What is the first derivative of 6(4e^{x^2}x^3+6e^{x^2}x) ?
The first derivative of 6(4e^{x^2}x^3+6e^{x^2}x) is 6(8e^{x^2}x^4+24e^{x^2}x^2+6e^{x^2})