What is the derivative of 2^{x^3+3x} ?

The derivative of 2^{x^3+3x} is ln(2)*2^{x^3+3x}(3x^2+3)

What is the first derivative of 2^{x^3+3x} ?

The first derivative of 2^{x^3+3x} is ln(2)*2^{x^3+3x}(3x^2+3)

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

ln (2) \cdot 2^{x^{3} + 3 x} (3 x^{2} + 3)

Solution steps

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

Apply exponent rule:

a^{b} = e^{b l n (a)}

2^{x^{3} + 3 x} = e^{(x^{3} + 3 x) l n (2)}

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

Apply the chain rule:

e^{(x^{3} + 3 x) l n (2)} \frac{d}{d x} ((x^{3} + 3 x) ln (2))

= e^{(x^{3} + 3 x) l n (2)} \frac{d}{d x} ((x^{3} + 3 x) ln (2))

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

= e^{(x^{3} + 3 x) l n (2)} ln (2) (3 x^{2} + 3)

e^{(x^{3} + 3 x) l n (2)} = 2^{x^{3} + 3 x}

= ln (2) \cdot 2^{x^{3} + 3 x} (3 x^{2} + 3)

What is the derivative of 2^{x^3+3x} ?
The derivative of 2^{x^3+3x} is ln(2)*2^{x^3+3x}(3x^2+3)
What is the first derivative of 2^{x^3+3x} ?
The first derivative of 2^{x^3+3x} is ln(2)*2^{x^3+3x}(3x^2+3)