What is the derivative of (x+(x+sin^2(x)^3)^4) ?

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

What is the first derivative of (x+(x+sin^2(x)^3)^4) ?

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

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\frac{d}{d x} ((x + (x + sin^{2} (x))^{3})^{4})

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

Solution steps

\frac{d}{d x} ((x + (x + sin^{2} (x))^{3})^{4})

Apply the chain rule:

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

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

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

x \to - 4 lim (\frac{x ^{2}}{4 x + 16})

\int_{- \frac{1}{3}}^{\frac{1}{3}} \frac{1}{1 - x ^{2}} d x

\int sin (x^{\frac{1}{2}}) d x

\frac{\partial}{\partial y} (x ln (y))

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