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

The derivative of [x+(x+sin^2(x)^6]^5) is 5(x+(x+sin^2(x))^6)^4(1+6(x+sin^2(x))^5(1+sin(2x)))

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

The first derivative of [x+(x+sin^2(x)^6]^5) is 5(x+(x+sin^2(x))^6)^4(1+6(x+sin^2(x))^5(1+sin(2x)))

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

5 (x + (x + sin^{2} (x))^{6})^{4} (1 + 6 (x + sin^{2} (x))^{5} (1 + sin (2 x)))

Solution steps

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

Apply the chain rule:

5 (x + (x + sin^{2} (x))^{6})^{4} \frac{d}{d x} (x + (x + sin^{2} (x))^{6})

= 5 (x + (x + sin^{2} (x))^{6})^{4} \frac{d}{d x} (x + (x + sin^{2} (x))^{6})

\frac{d}{d x} (x + (x + sin^{2} (x))^{6}) = 1 + 6 (x + sin^{2} (x))^{5} (1 + sin (2 x))

= 5 (x + (x + sin^{2} (x))^{6})^{4} (1 + 6 (x + sin^{2} (x))^{5} (1 + sin (2 x)))

What is the derivative of [x+(x+sin^2(x)^6]^5) ?
The derivative of [x+(x+sin^2(x)^6]^5) is 5(x+(x+sin^2(x))^6)^4(1+6(x+sin^2(x))^5(1+sin(2x)))
What is the first derivative of [x+(x+sin^2(x)^6]^5) ?
The first derivative of [x+(x+sin^2(x)^6]^5) is 5(x+(x+sin^2(x))^6)^4(1+6(x+sin^2(x))^5(1+sin(2x)))