What is expand 1/90 (e^{8x}+8e^{8x}x) ?

The solution to expand 1/90 (e^{8x}+8e^{8x}x) is 1/90 e^{8x}+(4e^{8x}x)/(45)

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expand 1/90 (e^{8x}+8e^{8x}x)

expand

\frac{1}{90} (e^{8 x} + 8 e^{8 x} x)

\frac{1}{90} e^{8 x} + \frac{4 e ^{8 x} x}{45}

Solution steps

\frac{1}{90} (e^{8 x} + 8 e^{8 x} x)

Apply the distributive law:

a (b + c) = ab + a c

a = \frac{1}{90}, b = e^{8 x}, c = 8 e^{8 x} x

= \frac{1}{90} e^{8 x} + \frac{1}{90} \cdot 8 e^{8 x} x

= \frac{1}{90} e^{8 x} + 8 \cdot \frac{1}{90} e^{8 x} x

Simplify

\frac{1}{90} e^{8 x} + 8 \cdot \frac{1}{90} e^{8 x} x : \frac{1}{90} e^{8 x} + \frac{4 e ^{8 x} x}{45}

= \frac{1}{90} e^{8 x} + \frac{4 e ^{8 x} x}{45}

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What is expand 1/90 (e^{8x}+8e^{8x}x) ?
The solution to expand 1/90 (e^{8x}+8e^{8x}x) is 1/90 e^{8x}+(4e^{8x}x)/(45)