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Popular >

derivative of y=x^6cos(x)

Solution

derivative of

y = x^{6} cos (x)

Solution

6 x^{5} cos (x) - x^{6} sin (x)

Solution steps

\frac{d}{d x} (x^{6} cos (x))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{6}, g = cos (x)

= \frac{d}{d x} (x^{6}) cos (x) + \frac{d}{d x} (cos (x)) x^{6}

\frac{d}{d x} (x^{6}) = 6 x^{5}

\frac{d}{d x} (cos (x)) = - sin (x)

= 6 x^{5} cos (x) + (- sin (x)) x^{6}

Simplify

= 6 x^{5} cos (x) - x^{6} sin (x)

Popular Examples

e^x(y^3+xy^3+1)dx+3y^2(xe^x-6)dy=0

e^{x} (y^{3} + x y^{3} + 1) d x + 3 y^{2} (x e^{x} - 6) d y = 0

slope of (-7,6),(9,-6/7)slope

(- 7, 6), (9, - \frac{6}{7})

derivative of f(x)=3x^2-4/x+4/(sqrt(x))derivative of

f (x) = 3 x^{2} - \frac{4}{x} + \frac{4}{x}

(dy)/(dx)=sec^2(x)

\frac{d y}{d x} = sec^{2} (x)

limit as x approaches infinity of 3x-x^2

x \to \infty lim (3 x - x^{2})

Frequently Asked Questions (FAQ)

What is the derivative of y=x^6cos(x) ?
The derivative of y=x^6cos(x) is 6x^5cos(x)-x^6sin(x)
What is the first derivative of y=x^6cos(x) ?
The first derivative of y=x^6cos(x) is 6x^5cos(x)-x^6sin(x)