What is the derivative of [x+(x+sin^2(x))^3]^6 ?

The derivative of [x+(x+sin^2(x))^3]^6 is 6(x+(x+sin^2(x))^3)^5(1+3(x+sin^2(x))^2(1+sin(2x)))

What is the first derivative of [x+(x+sin^2(x))^3]^6 ?

The first derivative of [x+(x+sin^2(x))^3]^6 is 6(x+(x+sin^2(x))^3)^5(1+3(x+sin^2(x))^2(1+sin(2x)))

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derivative of

[x + (x + sin^{2} (x))^{3}]^{6}

6 (x + (x + sin^{2} (x))^{3})^{5} (1 + 3 (x + sin^{2} (x))^{2} (1 + sin (2 x)))

Solution steps

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

Apply the chain rule:

6 (x + (x + sin^{2} (x))^{3})^{5} \frac{d}{d x} (x + (x + sin^{2} (x))^{3})

= 6 (x + (x + sin^{2} (x))^{3})^{5} \frac{d}{d x} (x + (x + sin^{2} (x))^{3})

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

= 6 (x + (x + sin^{2} (x))^{3})^{5} (1 + 3 (x + sin^{2} (x))^{2} (1 + sin (2 x)))

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What is the derivative of [x+(x+sin^2(x))^3]^6 ?
The derivative of [x+(x+sin^2(x))^3]^6 is 6(x+(x+sin^2(x))^3)^5(1+3(x+sin^2(x))^2(1+sin(2x)))
What is the first derivative of [x+(x+sin^2(x))^3]^6 ?
The first derivative of [x+(x+sin^2(x))^3]^6 is 6(x+(x+sin^2(x))^3)^5(1+3(x+sin^2(x))^2(1+sin(2x)))