What is (\partial)/(\partial x)(cos^7(x^4y^9)) ?

The answer to (\partial)/(\partial x)(cos^7(x^4y^9)) is -28x^3y^9cos^6(x^4y^9)sin(x^4y^9)

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(\partial)/(\partial x)(cos^7(x^4y^9))

\frac{\partial}{\partial x} (cos^{7} (x^{4} y^{9}))

- 28 x^{3} y^{9} cos^{6} (x^{4} y^{9}) sin (x^{4} y^{9})

Solution steps

\frac{\partial}{\partial x} (cos^{7} (x^{4} y^{9}))

Treat

y

as a constant

Apply the chain rule:

7 (cos (x^{4} y^{9}))^{6} \frac{\partial}{\partial x} (cos (x^{4} y^{9}))

= 7 (cos (x^{4} y^{9}))^{6} \frac{\partial}{\partial x} (cos (x^{4} y^{9}))

\frac{\partial}{\partial x} (cos (x^{4} y^{9})) = - sin (x^{4} y^{9}) \cdot 4 y^{9} x^{3}

= 7 (cos (x^{4} y^{9}))^{6} (- sin (x^{4} y^{9}) \cdot 4 y^{9} x^{3})

Simplify

= - 28 x^{3} y^{9} cos^{6} (x^{4} y^{9}) sin (x^{4} y^{9})

n = 1 \sum \infty (1 + \frac{1}{n})^{- n}

\frac{d}{d x} (sin^{4} (2 x co) s^{4} 3 x)

\int sec^{2} (x) + 3 d x

\frac{7}{s ( s ^{2} + 5 s )}

f (x) = x^{t a n (x)}

What is (\partial)/(\partial x)(cos^7(x^4y^9)) ?
The answer to (\partial)/(\partial x)(cos^7(x^4y^9)) is -28x^3y^9cos^6(x^4y^9)sin(x^4y^9)