What is expand 7(x^2+e^{2x})^6 derivative of x^2+e^{2x} ?

The solution to expand 7(x^2+e^{2x})^6 derivative of x^2+e^{2x} is

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expand 7(x^2+e^{2x})^6 derivative of x^2+e^{2x}

expand

7 (x^{2} + e^{2 x})^{6} \frac{d}{d x} (x^{2} + e^{2 x})

7 x^{12} \frac{d}{d x} (x^{2} + e^{2 x}) + 42 e^{2 x} x^{10} \frac{d}{d x} (x^{2} + e^{2 x}) + 105 e^{4 x} x^{8} \frac{d}{d x} (x^{2} + e^{2 x}) + 140 e^{6 x} x^{6} \frac{d}{d x} (x^{2} + e^{2 x}) + 105 e^{8 x} x^{4} \frac{d}{d x} (x^{2} + e^{2 x}) + 42 e^{10 x} x^{2} \frac{d}{d x} (x^{2} + e^{2 x}) + 7 e^{12 x} \frac{d}{d x} (x^{2} + e^{2 x})

Solution steps

7 (x^{2} + e^{2 x})^{6} \frac{d}{d x} (x^{2} + e^{2 x})

(x^{2} + e^{2 x})^{6} = x^{12} + 6 e^{2 x} x^{10} + 15 e^{4 x} x^{8} + 20 e^{6 x} x^{6} + 15 e^{8 x} x^{4} + 6 e^{10 x} x^{2} + e^{12 x}

= 7 (x^{12} + 6 e^{2 x} x^{10} + 15 e^{4 x} x^{8} + 20 e^{6 x} x^{6} + 15 e^{8 x} x^{4} + 6 e^{10 x} x^{2} + e^{12 x}) \frac{d}{d x} (x^{2} + e^{2 x})

Distribute parentheses

= 7 \frac{d}{d x} (x^{2} + e^{2 x}) x^{12} + 7 \frac{d}{d x} (x^{2} + e^{2 x}) 6 e^{2 x} x^{10} + 7 \frac{d}{d x} (x^{2} + e^{2 x}) 15 e^{4 x} x^{8} + 7 \frac{d}{d x} (x^{2} + e^{2 x}) 20 e^{6 x} x^{6} + 7 \frac{d}{d x} (x^{2} + e^{2 x}) 15 e^{8 x} x^{4} + 7 \frac{d}{d x} (x^{2} + e^{2 x}) 6 e^{10 x} x^{2} + 7 \frac{d}{d x} (x^{2} + e^{2 x}) e^{12 x}

= 7 x^{12} \frac{d}{d x} (x^{2} + e^{2 x}) + 7 \cdot 6 e^{2 x} x^{10} \frac{d}{d x} (x^{2} + e^{2 x}) + 7 \cdot 15 e^{4 x} x^{8} \frac{d}{d x} (x^{2} + e^{2 x}) + 7 \cdot 20 e^{6 x} x^{6} \frac{d}{d x} (x^{2} + e^{2 x}) + 7 \cdot 15 e^{8 x} x^{4} \frac{d}{d x} (x^{2} + e^{2 x}) + 7 \cdot 6 e^{10 x} x^{2} \frac{d}{d x} (x^{2} + e^{2 x}) + 7 e^{12 x} \frac{d}{d x} (x^{2} + e^{2 x})

Simplify

7 x^{12} \frac{d}{d x} (x^{2} + e^{2 x}) + 7 \cdot 6 e^{2 x} x^{10} \frac{d}{d x} (x^{2} + e^{2 x}) + 7 \cdot 15 e^{4 x} x^{8} \frac{d}{d x} (x^{2} + e^{2 x}) + 7 \cdot 20 e^{6 x} x^{6} \frac{d}{d x} (x^{2} + e^{2 x}) + 7 \cdot 15 e^{8 x} x^{4} \frac{d}{d x} (x^{2} + e^{2 x}) + 7 \cdot 6 e^{10 x} x^{2} \frac{d}{d x} (x^{2} + e^{2 x}) + 7 e^{12 x} \frac{d}{d x} (x^{2} + e^{2 x}) : 7 x^{12} \frac{d}{d x} (x^{2} + e^{2 x}) + 42 e^{2 x} x^{10} \frac{d}{d x} (x^{2} + e^{2 x}) + 105 e^{4 x} x^{8} \frac{d}{d x} (x^{2} + e^{2 x}) + 140 e^{6 x} x^{6} \frac{d}{d x} (x^{2} + e^{2 x}) + 105 e^{8 x} x^{4} \frac{d}{d x} (x^{2} + e^{2 x}) + 42 e^{10 x} x^{2} \frac{d}{d x} (x^{2} + e^{2 x}) + 7 e^{12 x} \frac{d}{d x} (x^{2} + e^{2 x})

= 7 x^{12} \frac{d}{d x} (x^{2} + e^{2 x}) + 42 e^{2 x} x^{10} \frac{d}{d x} (x^{2} + e^{2 x}) + 105 e^{4 x} x^{8} \frac{d}{d x} (x^{2} + e^{2 x}) + 140 e^{6 x} x^{6} \frac{d}{d x} (x^{2} + e^{2 x}) + 105 e^{8 x} x^{4} \frac{d}{d x} (x^{2} + e^{2 x}) + 42 e^{10 x} x^{2} \frac{d}{d x} (x^{2} + e^{2 x}) + 7 e^{12 x} \frac{d}{d x} (x^{2} + e^{2 x})

4 (1 - x - y)^{2}

(- 1 + 2 i)^{9}

5 (6 x cos (9 x) - 54 x^{2} sin (9 x) - 81 x^{3} cos (9 x))

5 l e f t (x + y + z - w)

(- 1 + 2 i)^{7}

What is expand 7(x^2+e^{2x})^6 derivative of x^2+e^{2x} ?
The solution to expand 7(x^2+e^{2x})^6 derivative of x^2+e^{2x} is