What is (\partial)/(\partial x)(cos(x^8+y^8)) ?

The answer to (\partial)/(\partial x)(cos(x^8+y^8)) is -sin(x^8+y^8)*8x^7

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(\partial)/(\partial x)(cos(x^8+y^8))

\frac{\partial}{\partial x} (cos (x^{8} + y^{8}))

- sin (x^{8} + y^{8}) \cdot 8 x^{7}

Solution steps

\frac{\partial}{\partial x} (cos (x^{8} + y^{8}))

Treat

y

as a constant

Apply the chain rule:

- sin (x^{8} + y^{8}) \frac{\partial}{\partial x} (x^{8} + y^{8})

= - sin (x^{8} + y^{8}) \frac{\partial}{\partial x} (x^{8} + y^{8})

\frac{\partial}{\partial x} (x^{8} + y^{8}) = 8 x^{7}

= - sin (x^{8} + y^{8}) \cdot 8 x^{7}

\frac{d}{d x} (5 x + 8)

\frac{1}{A ^{2} A}

\frac{\partial}{\partial x} (4 x ln (y) + y ln (z) - x)

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

\frac{d}{d x} (cot (2 x^{2} - 1))

What is (\partial)/(\partial x)(cos(x^8+y^8)) ?
The answer to (\partial)/(\partial x)(cos(x^8+y^8)) is -sin(x^8+y^8)*8x^7