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

The derivative of [x+(x+sin^2(x))^5]^3 is 3(x+(x+sin^2(x))^5)^2(1+5(x+sin^2(x))^4(1+sin(2x)))

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

The first derivative of [x+(x+sin^2(x))^5]^3 is 3(x+(x+sin^2(x))^5)^2(1+5(x+sin^2(x))^4(1+sin(2x)))

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derivative of

[x + (x + sin^{2} (x))^{5}]^{3}

3 (x + (x + sin^{2} (x))^{5})^{2} (1 + 5 (x + sin^{2} (x))^{4} (1 + sin (2 x)))

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (x + (x + sin^{2} (x))^{5}) = 1 + 5 (x + sin^{2} (x))^{4} (1 + sin (2 x))

= 3 (x + (x + sin^{2} (x))^{5})^{2} (1 + 5 (x + sin^{2} (x))^{4} (1 + sin (2 x)))

What is the derivative of [x+(x+sin^2(x))^5]^3 ?
The derivative of [x+(x+sin^2(x))^5]^3 is 3(x+(x+sin^2(x))^5)^2(1+5(x+sin^2(x))^4(1+sin(2x)))
What is the first derivative of [x+(x+sin^2(x))^5]^3 ?
The first derivative of [x+(x+sin^2(x))^5]^3 is 3(x+(x+sin^2(x))^5)^2(1+5(x+sin^2(x))^4(1+sin(2x)))