What is the derivative of [x+(x+sin^2(x))^5]^7 ?

The derivative of [x+(x+sin^2(x))^5]^7 is 7(x+(x+sin^2(x))^5)^6(1+5(x+sin^2(x))^4(1+sin(2x)))

What is the first derivative of [x+(x+sin^2(x))^5]^7 ?

The first derivative of [x+(x+sin^2(x))^5]^7 is 7(x+(x+sin^2(x))^5)^6(1+5(x+sin^2(x))^4(1+sin(2x)))

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derivative of

[x + (x + sin^{2} (x))^{5}]^{7}

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

Solution steps

\frac{d}{d x} ((x + (x + sin^{2} (x))^{5})^{7})

Apply the chain rule:

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

= 7 (x + (x + sin^{2} (x))^{5})^{6} \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))

= 7 (x + (x + sin^{2} (x))^{5})^{6} (1 + 5 (x + sin^{2} (x))^{4} (1 + sin (2 x)))

What is the derivative of [x+(x+sin^2(x))^5]^7 ?
The derivative of [x+(x+sin^2(x))^5]^7 is 7(x+(x+sin^2(x))^5)^6(1+5(x+sin^2(x))^4(1+sin(2x)))
What is the first derivative of [x+(x+sin^2(x))^5]^7 ?
The first derivative of [x+(x+sin^2(x))^5]^7 is 7(x+(x+sin^2(x))^5)^6(1+5(x+sin^2(x))^4(1+sin(2x)))