derivative of 3^{x^4-2x^2} — step-by-step solution

⚠ 2x is read as the product 2*x: for a power, write 2^x‖3^{x^4-2x^2} is read as 3^(x^4-2x^2)

Let's perform the differentiation:

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

You can convert the expression:

3^{(x^{4} - 2 x^{2})}

into:

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

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

ℹ

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

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

‖

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

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

‖

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

3^{(x^{4} - 2 x^{2})}

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

ℹ

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

4 x^{3}

‖

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

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

‖

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

2 x

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

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

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

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

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

▶Derivative:

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