What is the derivative of 2A+B(e^xx^2+4e^xx+2e^x) ?

The derivative of 2A+B(e^xx^2+4e^xx+2e^x) is B(e^xx^2+6e^xx+6e^x)

What is the first derivative of 2A+B(e^xx^2+4e^xx+2e^x) ?

The first derivative of 2A+B(e^xx^2+4e^xx+2e^x) is B(e^xx^2+6e^xx+6e^x)

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\frac{d}{d x} (2 A + B (e^{x} x^{2} + 4 e^{x} x + 2 e^{x}))

B (e^{x} x^{2} + 6 e^{x} x + 6 e^{x})

Solution steps

\frac{d}{d x} (2 A + B (e^{x} x^{2} + 4 e^{x} x + 2 e^{x}))

Treat

A, B

as constants

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (2 A) = 0

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

= 0 + B (e^{x} x^{2} + 6 e^{x} x + 6 e^{x})

Simplify

= B (e^{x} x^{2} + 6 e^{x} x + 6 e^{x})

x y^{^{'}} + 2 y = 3 cos (x)

\int cos^{2} (2 x) sin^{3} (2 x) d x

h (x) = 4^{x} - 6

g (x) = 3 x^{2} cos (x) + 8 x

\int \frac{x}{( x ^{2} + 9 )} d x

What is the derivative of 2A+B(e^xx^2+4e^xx+2e^x) ?
The derivative of 2A+B(e^xx^2+4e^xx+2e^x) is B(e^xx^2+6e^xx+6e^x)
What is the first derivative of 2A+B(e^xx^2+4e^xx+2e^x) ?
The first derivative of 2A+B(e^xx^2+4e^xx+2e^x) is B(e^xx^2+6e^xx+6e^x)