Solved: "Find the derivatives of the given function. g(x)=e2xln⁡(x4)" - Plainmath

arenceabigns

Answered question

2021-10-02

Find the derivatives of the given function.

g (x) = e^{2 x} \ln (x^{4})

Answer & Explanation

au4gsf

Skilled2021-10-03Added 95 answers

Step 1 Given:

g (x) = e^{2 x} \ln (x^{4})

Step 2 Calculation:
Let us consider y=g(x)
Then,

y = e^{2 x} \ln (x^{4})

\frac{d y}{d x} = \frac{d}{d x} (e^{2 x} \ln (x^{4}))

Apply the Product Rule:

f = e^{2 x}, g = \ln (x^{4})

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

\frac{d}{d x} (e^{2 x}) = e^{2 x} \cdot 2

\frac{d}{d x} (\ln (x^{4})) = \frac{4}{x}

\frac{d}{d x} (e^{2 x} \ln (x^{4})) = e^{2 x} \cdot 2 \ln (x^{4}) + \frac{4}{x} e^{2 x}

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

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