What is the derivative of [x+(x+sin^2(x)^7]^3) ?

The derivative of [x+(x+sin^2(x)^7]^3) is 3(x+(x+sin^2(x))^7)^2(1+7(x+sin^2(x))^6(1+sin(2x)))

What is the first derivative of [x+(x+sin^2(x)^7]^3) ?

The first derivative of [x+(x+sin^2(x)^7]^3) is 3(x+(x+sin^2(x))^7)^2(1+7(x+sin^2(x))^6(1+sin(2x)))

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\frac{d}{d x} ([x + (x + sin^{2} (x))^{7}]^{3})

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

Solution steps

\frac{d}{d x} ((x + (x + sin^{2} (x))^{7})^{3})

Apply the chain rule:

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

= 3 (x + (x + sin^{2} (x))^{7})^{2} \frac{d}{d x} (x + (x + sin^{2} (x))^{7})

\frac{d}{d x} (x + (x + sin^{2} (x))^{7}) = 1 + 7 (x + sin^{2} (x))^{6} (1 + sin (2 x))

= 3 (x + (x + sin^{2} (x))^{7})^{2} (1 + 7 (x + sin^{2} (x))^{6} (1 + sin (2 x)))

x \to 0 lim (2^{- \frac{1}{x}})

\frac{\partial}{\partial y} (y + x cos (t))

\frac{d}{d x} (\frac{1}{x ^{2} + y ^{2}} + x e^{- y})

5 x^{3} - 4 x^{2} - 11

x \to - 3 - lim (\frac{1}{x + 3})

What is the derivative of [x+(x+sin^2(x)^7]^3) ?
The derivative of [x+(x+sin^2(x)^7]^3) is 3(x+(x+sin^2(x))^7)^2(1+7(x+sin^2(x))^6(1+sin(2x)))
What is the first derivative of [x+(x+sin^2(x)^7]^3) ?
The first derivative of [x+(x+sin^2(x)^7]^3) is 3(x+(x+sin^2(x))^7)^2(1+7(x+sin^2(x))^6(1+sin(2x)))