What is the derivative of sqrt(((x^2)2^x)^3) ?

The derivative of sqrt(((x^2)2^x)^3) is (3ln(2)*8^xx^6+3*2^{1+3x}x^5)/(2sqrt(x^6)\sqrt{8^x)}

What is the first derivative of sqrt(((x^2)2^x)^3) ?

The first derivative of sqrt(((x^2)2^x)^3) is (3ln(2)*8^xx^6+3*2^{1+3x}x^5)/(2sqrt(x^6)\sqrt{8^x)}

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derivative of

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

\frac{3 ln ( 2 ) \cdot 8 ^{x} x ^{6} + 3 \cdot 2 ^{1 + 3 x} x ^{5}}{2 x ^{6} 8 ^{x}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} ((x^{2} \cdot 2^{x})^{3}) = 3 ln (2) \cdot 8^{x} x^{6} + 3 \cdot 2^{1 + 3 x} x^{5}

= \frac{1}{2 ( x ^{2} \cdot 2 ^{x} ) ^{3}} (3 ln (2) \cdot 8^{x} x^{6} + 3 \cdot 2^{1 + 3 x} x^{5})

Simplify

\frac{1}{2 ( x ^{2} \cdot 2 ^{x} ) ^{3}} (3 ln (2) \cdot 8^{x} x^{6} + 3 \cdot 2^{1 + 3 x} x^{5}) : \frac{3 ln ( 2 ) \cdot 8 ^{x} x ^{6} + 3 \cdot 2 ^{1 + 3 x} x ^{5}}{2 x ^{6} 8 ^{x}}

= \frac{3 ln ( 2 ) \cdot 8 ^{x} x ^{6} + 3 \cdot 2 ^{1 + 3 x} x ^{5}}{2 x ^{6} 8 ^{x}}

What is the derivative of sqrt(((x^2)2^x)^3) ?
The derivative of sqrt(((x^2)2^x)^3) is (3ln(2)*8^xx^6+3*2^{1+3x}x^5)/(2sqrt(x^6)\sqrt{8^x)}
What is the first derivative of sqrt(((x^2)2^x)^3) ?
The first derivative of sqrt(((x^2)2^x)^3) is (3ln(2)*8^xx^6+3*2^{1+3x}x^5)/(2sqrt(x^6)\sqrt{8^x)}