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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

5 (x + (x + sin^{2} (x))^{7})^{4} \frac{d}{d x} (x + (x + sin^{2} (x))^{7})

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

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

\frac{d y}{d x} + \frac{1}{x} y = 10 x^{2}

\int x 1 - x^{2} - x^{2} d x

\int (x^{2} e^{- x^{3}}) d x

\frac{\partial}{\partial y} (x y z^{2} tan (y t))

y = 2 - 6 x, at x = - 1

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