What is the derivative of f(x)=sqrt(2e^{x^3)+1} ?

The derivative of f(x)=sqrt(2e^{x^3)+1} is (3e^{x^3}x^2)/(sqrt(2e^{x^3)+1)}

What is the first derivative of f(x)=sqrt(2e^{x^3)+1} ?

The first derivative of f(x)=sqrt(2e^{x^3)+1} is (3e^{x^3}x^2)/(sqrt(2e^{x^3)+1)}

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derivative of

f (x) = 2 e^{x^{3}} + 1

\frac{3 e ^{x^{3}} x ^{2}}{2 e ^{x^{3}} + 1}

Solution steps

\frac{d}{d x} (2 e^{x^{3}} + 1)

Apply the chain rule:

\frac{1}{2 2 e ^{x^{3}} + 1} \frac{d}{d x} (2 e^{x^{3}} + 1)

= \frac{1}{2 2 e ^{x^{3}} + 1} \frac{d}{d x} (2 e^{x^{3}} + 1)

\frac{d}{d x} (2 e^{x^{3}} + 1) = 6 e^{x^{3}} x^{2}

= \frac{1}{2 2 e ^{x^{3}} + 1} \cdot 6 e^{x^{3}} x^{2}

Simplify

\frac{1}{2 2 e ^{x^{3}} + 1} \cdot 6 e^{x^{3}} x^{2} : \frac{3 e ^{x^{3}} x ^{2}}{2 e ^{x^{3}} + 1}

= \frac{3 e ^{x^{3}} x ^{2}}{2 e ^{x^{3}} + 1}

What is the derivative of f(x)=sqrt(2e^{x^3)+1} ?
The derivative of f(x)=sqrt(2e^{x^3)+1} is (3e^{x^3}x^2)/(sqrt(2e^{x^3)+1)}
What is the first derivative of f(x)=sqrt(2e^{x^3)+1} ?
The first derivative of f(x)=sqrt(2e^{x^3)+1} is (3e^{x^3}x^2)/(sqrt(2e^{x^3)+1)}