What is (\partial)/(\partial x)(cos(x^5+y)) ?

The answer to (\partial)/(\partial x)(cos(x^5+y)) is -sin(x^5+y)*5x^4

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(\partial)/(\partial x)(cos(x^5+y))

\frac{\partial}{\partial x} (cos (x^{5} + y))

- sin (x^{5} + y) \cdot 5 x^{4}

Solution steps

\frac{\partial}{\partial x} (cos (x^{5} + y))

Treat

y

as a constant

Apply the chain rule:

- sin (x^{5} + y) \frac{\partial}{\partial x} (x^{5} + y)

= - sin (x^{5} + y) \frac{\partial}{\partial x} (x^{5} + y)

\frac{\partial}{\partial x} (x^{5} + y) = 5 x^{4}

= - sin (x^{5} + y) \cdot 5 x^{4}

d er i v a t i v e f (x) = \frac{( x + 3 ) ( x + 1 )}{x ^{2} - 49}

d er i v a t i v e y = ln (x + x^{2} + 6)

t a y l or x^{\frac{1}{4}}, 16

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

f (x) = \frac{1}{1 + x}

What is (\partial)/(\partial x)(cos(x^5+y)) ?
The answer to (\partial)/(\partial x)(cos(x^5+y)) is -sin(x^5+y)*5x^4