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

The derivative of [x+(x+sin^2(x)^3]^6) is 6(x+(x+sin^2(x))^3)^5(1+3(x+sin^2(x))^2(1+sin(2x)))

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

The first derivative of [x+(x+sin^2(x)^3]^6) is 6(x+(x+sin^2(x))^3)^5(1+3(x+sin^2(x))^2(1+sin(2x)))

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\frac{d}{d x} ([x + (x + sin^{2} (x))^{3}]^{6})

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

Solution steps

\frac{d}{d x} ((x + (x + sin^{2} (x))^{3})^{6})

Apply the chain rule:

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

= 6 (x + (x + sin^{2} (x))^{3})^{5} \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))

= 6 (x + (x + sin^{2} (x))^{3})^{5} (1 + 3 (x + sin^{2} (x))^{2} (1 + sin (2 x)))

\int 2^{e^{x}} (1 + 2^{e^{x}})^{5} e^{x} d x

\frac{d}{d x} (\frac{sec ( x )}{x})

\frac{d}{d x} ((ln (3))^{x})

\int \frac{x}{2} d x

f (x) = 3 x^{2} + 9 x^{3} - 5 x, at x = - 4

What is the derivative of [x+(x+sin^2(x)^3]^6) ?
The derivative of [x+(x+sin^2(x)^3]^6) is 6(x+(x+sin^2(x))^3)^5(1+3(x+sin^2(x))^2(1+sin(2x)))
What is the first derivative of [x+(x+sin^2(x)^3]^6) ?
The first derivative of [x+(x+sin^2(x)^3]^6) is 6(x+(x+sin^2(x))^3)^5(1+3(x+sin^2(x))^2(1+sin(2x)))