What is the derivative of 2^{3x^4-3x} ?

The derivative of 2^{3x^4-3x} is ln(2)*2^{3x^4-3x}(12x^3-3)

What is the first derivative of 2^{3x^4-3x} ?

The first derivative of 2^{3x^4-3x} is ln(2)*2^{3x^4-3x}(12x^3-3)

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\frac{d}{d x} (2^{3 x^{4} - 3 x})

ln (2) \cdot 2^{3 x^{4} - 3 x} (12 x^{3} - 3)

Solution steps

\frac{d}{d x} (2^{3 x^{4} - 3 x})

Apply exponent rule:

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

2^{3 x^{4} - 3 x} = e^{(3 x^{4} - 3 x) l n (2)}

= \frac{d}{d x} (e^{(3 x^{4} - 3 x) l n (2)})

Apply the chain rule:

e^{(3 x^{4} - 3 x) l n (2)} \frac{d}{d x} ((3 x^{4} - 3 x) ln (2))

= e^{(3 x^{4} - 3 x) l n (2)} \frac{d}{d x} ((3 x^{4} - 3 x) ln (2))

\frac{d}{d x} ((3 x^{4} - 3 x) ln (2)) = ln (2) (12 x^{3} - 3)

= e^{(3 x^{4} - 3 x) l n (2)} ln (2) (12 x^{3} - 3)

e^{(3 x^{4} - 3 x) l n (2)} = 2^{3 x^{4} - 3 x}

= ln (2) \cdot 2^{3 x^{4} - 3 x} (12 x^{3} - 3)

\frac{\partial}{\partial x} (\frac{( 2 x - 4 y )}{2 x + 4 y})

\int sin^{- 2} (x) d x

\frac{d}{d x} (20 - x^{2})

x \to 6 lim (f (x))

\int \frac{t}{1 - t ^{3}} d t

What is the derivative of 2^{3x^4-3x} ?
The derivative of 2^{3x^4-3x} is ln(2)*2^{3x^4-3x}(12x^3-3)
What is the first derivative of 2^{3x^4-3x} ?
The first derivative of 2^{3x^4-3x} is ln(2)*2^{3x^4-3x}(12x^3-3)