Find $\frac { d y } { d x }$ if $y = x ^ { 4 } e ^ { x ^ { 10 } }$ .
A) $\frac { d y } { d x } = e ^ { x ^ { 10 } } \left( \frac { x ^ { 5 } } { 5 } + \frac { x ^ { 11 } } { 11 } \right)$
B) $\frac { d y } { d x } = e ^ { x ^ { 10 } } \left( x ^ { 4 } + x ^ { 10 } \right)$
C) $\frac { d y } { d x } = e ^ { x ^ { 10 } } \left( 4 x ^ { 3 } + 10 x ^ { 13 } \right)$
D) $\frac { d y } { d x } = 4 x ^ { 3 } e ^ { x ^ { 10 } - 1 }$
E) $\frac { d y } { d x } = 4 x ^ { 3 } e ^ { x ^ { 10 } }$

Question

Quizplus · Accepted Answer

To find $\frac{dy}{dx}$ for $y = x^4e^{x^{10}}$, we use the product rule $d(uv) = u \, dv + v \, du$ and the chain rule for differentiation. Differentiating $x^4$ gives $4x^3$, and differentiating $e^{x^{10}}$ gives $e^{x^{10}} \cdot 10x^9$ (using the chain rule). Thus, $\frac{dy}{dx} = x^4 \cdot 10x^9 \cdot e^{x^{10}} + e^{x^{10}} \cdot 4x^3 = e^{x^{10}}(4x^3 + 10x^{13})$.

Find dydx\frac { d y } { d x }dxdy​ If y=x4ex10y = x ^ { 4 } e ^ { x ^ { 10 } }y=x4ex10

Find $\frac { d y } { d x }$ If $y = x ^ { 4 } e ^ { x ^ { 10 } }$