What is the derivative of (2+(x^2+1^4)^3) ?

The derivative of (2+(x^2+1^4)^3) is 3(x^8+4x^6+6x^4+4x^2+3)^2(8x^7+24x^5+24x^3+8x)

What is the first derivative of (2+(x^2+1^4)^3) ?

The first derivative of (2+(x^2+1^4)^3) is 3(x^8+4x^6+6x^4+4x^2+3)^2(8x^7+24x^5+24x^3+8x)

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

3 (x^{8} + 4 x^{6} + 6 x^{4} + 4 x^{2} + 3)^{2} (8 x^{7} + 24 x^{5} + 24 x^{3} + 8 x)

Solution steps

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

Simplify

(2 + (x^{2} + 1)^{4})^{3} : (x^{8} + 4 x^{6} + 6 x^{4} + 4 x^{2} + 3)^{3}

= \frac{d}{d x} ((x^{8} + 4 x^{6} + 6 x^{4} + 4 x^{2} + 3)^{3})

Apply the chain rule:

3 (x^{8} + 4 x^{6} + 6 x^{4} + 4 x^{2} + 3)^{2} \frac{d}{d x} (x^{8} + 4 x^{6} + 6 x^{4} + 4 x^{2} + 3)

= 3 (x^{8} + 4 x^{6} + 6 x^{4} + 4 x^{2} + 3)^{2} \frac{d}{d x} (x^{8} + 4 x^{6} + 6 x^{4} + 4 x^{2} + 3)

\frac{d}{d x} (x^{8} + 4 x^{6} + 6 x^{4} + 4 x^{2} + 3) = 8 x^{7} + 24 x^{5} + 24 x^{3} + 8 x

= 3 (x^{8} + 4 x^{6} + 6 x^{4} + 4 x^{2} + 3)^{2} (8 x^{7} + 24 x^{5} + 24 x^{3} + 8 x)

What is the derivative of (2+(x^2+1^4)^3) ?
The derivative of (2+(x^2+1^4)^3) is 3(x^8+4x^6+6x^4+4x^2+3)^2(8x^7+24x^5+24x^3+8x)
What is the first derivative of (2+(x^2+1^4)^3) ?
The first derivative of (2+(x^2+1^4)^3) is 3(x^8+4x^6+6x^4+4x^2+3)^2(8x^7+24x^5+24x^3+8x)