What is the derivative of 3^{(x^4+1^3}) ?

The derivative of 3^{(x^4+1^3}) is 4ln(3)*3^{(x^4+1)^3+1}x^3(x^4+1)^2

What is the first derivative of 3^{(x^4+1^3}) ?

The first derivative of 3^{(x^4+1^3}) is 4ln(3)*3^{(x^4+1)^3+1}x^3(x^4+1)^2

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\frac{d}{d x} (3^{(x^{4} + 1)^{3}})

4 ln (3) \cdot 3^{(x^{4} + 1)^{3} + 1} x^{3} (x^{4} + 1)^{2}

Solution steps

\frac{d}{d x} (3^{(x^{4} + 1)^{3}})

Apply exponent rule:

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

3^{(x^{4} + 1)^{3}} = e^{(x^{4} + 1)^{3} l n (3)}

= \frac{d}{d x} (e^{(x^{4} + 1)^{3} l n (3)})

Apply the chain rule:

e^{(x^{4} + 1)^{3} l n (3)} \frac{d}{d x} ((x^{4} + 1)^{3} ln (3))

= e^{(x^{4} + 1)^{3} l n (3)} \frac{d}{d x} ((x^{4} + 1)^{3} ln (3))

\frac{d}{d x} ((x^{4} + 1)^{3} ln (3)) = 12 ln (3) x^{3} (x^{4} + 1)^{2}

= e^{(x^{4} + 1)^{3} l n (3)} \cdot 12 ln (3) x^{3} (x^{4} + 1)^{2}

Simplify

e^{(x^{4} + 1)^{3} l n (3)} \cdot 12 ln (3) x^{3} (x^{4} + 1)^{2} : 4 ln (3) \cdot 3^{(x^{4} + 1)^{3} + 1} x^{3} (x^{4} + 1)^{2}

= 4 ln (3) \cdot 3^{(x^{4} + 1)^{3} + 1} x^{3} (x^{4} + 1)^{2}

What is the derivative of 3^{(x^4+1^3}) ?
The derivative of 3^{(x^4+1^3}) is 4ln(3)*3^{(x^4+1)^3+1}x^3(x^4+1)^2
What is the first derivative of 3^{(x^4+1^3}) ?
The first derivative of 3^{(x^4+1^3}) is 4ln(3)*3^{(x^4+1)^3+1}x^3(x^4+1)^2