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

The derivative of [x+(x+sin^2(x)^3]^5) is 5(x+(x+sin^2(x))^3)^4(1+3(x+sin^2(x))^2(1+sin(2x)))

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

The first derivative of [x+(x+sin^2(x)^3]^5) is 5(x+(x+sin^2(x))^3)^4(1+3(x+sin^2(x))^2(1+sin(2x)))

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

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

Solution steps

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

Apply the chain rule:

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

= 5 (x + (x + sin^{2} (x))^{3})^{4} \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))

= 5 (x + (x + sin^{2} (x))^{3})^{4} (1 + 3 (x + sin^{2} (x))^{2} (1 + sin (2 x)))

\int_{0}^{1} 2^{- x} d x

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

\frac{d y}{d x} = (\frac{( 2 y + 7 )}{8 x + 9})^{2}

\int_{0}^{2} (6 t i - t^{3} j + 5 t^{9} k) d t

x \to 0 lim (\frac{x + 5}{3 x})

What is the derivative of [x+(x+sin^2(x)^3]^5) ?
The derivative of [x+(x+sin^2(x)^3]^5) is 5(x+(x+sin^2(x))^3)^4(1+3(x+sin^2(x))^2(1+sin(2x)))
What is the first derivative of [x+(x+sin^2(x)^3]^5) ?
The first derivative of [x+(x+sin^2(x)^3]^5) is 5(x+(x+sin^2(x))^3)^4(1+3(x+sin^2(x))^2(1+sin(2x)))