What is the d/(dy)((ye^{3y}+e^{5y})^9) ?

The d/(dy)((ye^{3y}+e^{5y})^9) is 9(ye^{3y}+e^{5y})^8(e^{3y}+3e^{3y}y+e^{5y}*5)

What is the first d/(dy)((ye^{3y}+e^{5y})^9) ?

The first d/(dy)((ye^{3y}+e^{5y})^9) is 9(ye^{3y}+e^{5y})^8(e^{3y}+3e^{3y}y+e^{5y}*5)

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\frac{d}{d y} ((y e^{3 y} + e^{5 y})^{9})

9 (y e^{3 y} + e^{5 y})^{8} (e^{3 y} + 3 e^{3 y} y + e^{5 y} \cdot 5)

Solution steps

\frac{d}{d y} ((y e^{3 y} + e^{5 y})^{9})

Apply the chain rule:

9 (y e^{3 y} + e^{5 y})^{8} \frac{d}{d y} (y e^{3 y} + e^{5 y})

= 9 (y e^{3 y} + e^{5 y})^{8} \frac{d}{d y} (y e^{3 y} + e^{5 y})

\frac{d}{d y} (y e^{3 y} + e^{5 y}) = e^{3 y} + 3 e^{3 y} y + e^{5 y} \cdot 5

= 9 (y e^{3 y} + e^{5 y})^{8} (e^{3 y} + 3 e^{3 y} y + e^{5 y} \cdot 5)

What is the d/(dy)((ye^{3y}+e^{5y})^9) ?
The d/(dy)((ye^{3y}+e^{5y})^9) is 9(ye^{3y}+e^{5y})^8(e^{3y}+3e^{3y}y+e^{5y}*5)
What is the first d/(dy)((ye^{3y}+e^{5y})^9) ?
The first d/(dy)((ye^{3y}+e^{5y})^9) is 9(ye^{3y}+e^{5y})^8(e^{3y}+3e^{3y}y+e^{5y}*5)