We have an answer to "Find the derivatives of the functions y=(9x2−6x+2)⋅ex3"

oliviayychengwh

Answered question

2021-12-06

Find the derivatives of the functions

y = (9 x^{2} - 6 x + 2) \cdot e^{x^{3}}

Jeremy Merritt

Beginner2021-12-07Added 31 answers

Given,

y = (9 x^{2} - 6 x + 2) \cdot e^{x^{3}}

Differentiating with respect to x, we get

\frac{d y}{d x} = \frac{d (9 x^{2} - 6 x + 2)}{d x} \cdot e^{x^{3}} + \frac{d (e^{x^{3}})}{d x} \cdot (9 x^{2} - 6 x + 2) [∵ \frac{d (u v)}{d x} = \frac{d u}{d x} \cdot v + \frac{d v}{d x} \cdot u]

\Rightarrow \frac{d y}{d x} = [9 (2 x) - 6 (1) + 0] * e^{x^{3}} + e^{x^{3}} * \frac{d (x^{3})}{d x} * (9 x^{2} - 6 x + 2) [\begin{matrix} ∵ \frac{d (x^{n})}{d x} * v + \frac{d v}{d x} * u \\ \frac{d (c)}{d x} = 0, c \in R \\ & \frac{d (e^{x})}{d x} = e^{x} \end{matrix}]

\Rightarrow \frac{d y}{d x} = (18 x - 6) \cdot e^{x^{3}} + e^{x^{3}} \cdot 3 x^{2} \cdot (9 x^{2} - 6 x + 2)

\Rightarrow \frac{d y}{d x} = e^{x^{3}} [18 x - 6 + 27 x^{4} - 18 x^{3} + 6 x^{2}]

\Rightarrow \frac{d y}{d x} = e^{x^{3}} [27 x^{4} - 18 x^{3} + 6 x^{2} + 18 x - 6]

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