What is the derivative of cos^9(x^2y^6) ?

The derivative of cos^9(x^2y^6) is -9cos^8(x^2y^6)sin(x^2y^6)(2xy^6+6x^2y^5(dy)/(dx))

What is the first derivative of cos^9(x^2y^6) ?

The first derivative of cos^9(x^2y^6) is -9cos^8(x^2y^6)sin(x^2y^6)(2xy^6+6x^2y^5(dy)/(dx))

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\frac{d}{d x} (cos^{9} (x^{2} y^{6}))

- 9 cos^{8} (x^{2} y^{6}) sin (x^{2} y^{6}) (2 x y^{6} + 6 x^{2} y^{5} \frac{d y}{d x})

Solution steps

\frac{d}{d x} (cos^{9} (x^{2} y^{6}))

Apply the chain rule:

9 (cos (x^{2} y^{6}))^{8} \frac{d}{d x} (cos (x^{2} y^{6}))

= 9 (cos (x^{2} y^{6}))^{8} \frac{d}{d x} (cos (x^{2} y^{6}))

\frac{d}{d x} (cos (x^{2} y^{6})) = - sin (x^{2} y^{6}) (2 x y^{6} + 6 y^{5} \frac{d y}{d x} x^{2})

= 9 (cos (x^{2} y^{6}))^{8} (- sin (x^{2} y^{6}) (2 x y^{6} + 6 y^{5} \frac{d y}{d x} x^{2}))

Simplify

= - 9 cos^{8} (x^{2} y^{6}) sin (x^{2} y^{6}) (2 x y^{6} + 6 x^{2} y^{5} \frac{d y}{d x})

14 x

x y^{3} + x y = 2, (1, 1)

f (x) = \frac{4}{x ^{2}}, at x = 1

\frac{d}{d x} (\frac{5 x ^{3} + 7 x ^{2}}{x})

\frac{d}{d x} (x - \frac{1}{9} x)

What is the derivative of cos^9(x^2y^6) ?
The derivative of cos^9(x^2y^6) is -9cos^8(x^2y^6)sin(x^2y^6)(2xy^6+6x^2y^5(dy)/(dx))
What is the first derivative of cos^9(x^2y^6) ?
The first derivative of cos^9(x^2y^6) is -9cos^8(x^2y^6)sin(x^2y^6)(2xy^6+6x^2y^5(dy)/(dx))