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Popular >

derivative of x^4cos(7x-5)

Solution

derivative of

x^{4} cos (7 x - 5)

Solution

4 x^{3} cos (7 x - 5) - 7 x^{4} sin (7 x - 5)

Solution steps

\frac{d}{d x} (x^{4} cos (7 x - 5))

Apply the Product Rule:

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

f = x^{4}, g = cos (7 x - 5)

= \frac{d}{d x} (x^{4}) cos (7 x - 5) + \frac{d}{d x} (cos (7 x - 5)) x^{4}

\frac{d}{d x} (x^{4}) = 4 x^{3}

\frac{d}{d x} (cos (7 x - 5)) = - sin (7 x - 5) \cdot 7

= 4 x^{3} cos (7 x - 5) + (- sin (7 x - 5) \cdot 7) x^{4}

Simplify

= 4 x^{3} cos (7 x - 5) - 7 x^{4} sin (7 x - 5)

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Frequently Asked Questions (FAQ)

What is the derivative of x^4cos(7x-5) ?
The derivative of x^4cos(7x-5) is 4x^3cos(7x-5)-7x^4sin(7x-5)
What is the first derivative of x^4cos(7x-5) ?
The first derivative of x^4cos(7x-5) is 4x^3cos(7x-5)-7x^4sin(7x-5)