What is the derivative of cos(5x^2-7x(10x-7)) ?

The derivative of cos(5x^2-7x(10x-7)) is -sin(5x^2-7x)(10x-7)^2+10cos(5x^2-7x)

What is the first derivative of cos(5x^2-7x(10x-7)) ?

The first derivative of cos(5x^2-7x(10x-7)) is -sin(5x^2-7x)(10x-7)^2+10cos(5x^2-7x)

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\frac{d}{d x} (cos (5 x^{2} - 7 x) (10 x - 7))

- sin (5 x^{2} - 7 x) (10 x - 7)^{2} + 10 cos (5 x^{2} - 7 x)

Solution steps

\frac{d}{d x} (cos (5 x^{2} - 7 x) (10 x - 7))

Apply the Product Rule:

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

f = cos (5 x^{2} - 7 x), g = 10 x - 7

= \frac{d}{d x} (cos (5 x^{2} - 7 x)) (10 x - 7) + \frac{d}{d x} (10 x - 7) cos (5 x^{2} - 7 x)

\frac{d}{d x} (cos (5 x^{2} - 7 x)) = - sin (5 x^{2} - 7 x) (10 x - 7)

\frac{d}{d x} (10 x - 7) = 10

= (- sin (5 x^{2} - 7 x) (10 x - 7)) (10 x - 7) + 10 cos (5 x^{2} - 7 x)

Simplify

(- sin (5 x^{2} - 7 x) (10 x - 7)) (10 x - 7) + 10 cos (5 x^{2} - 7 x) : - sin (5 x^{2} - 7 x) (10 x - 7)^{2} + 10 cos (5 x^{2} - 7 x)

= - sin (5 x^{2} - 7 x) (10 x - 7)^{2} + 10 cos (5 x^{2} - 7 x)

What is the derivative of cos(5x^2-7x(10x-7)) ?
The derivative of cos(5x^2-7x(10x-7)) is -sin(5x^2-7x)(10x-7)^2+10cos(5x^2-7x)
What is the first derivative of cos(5x^2-7x(10x-7)) ?
The first derivative of cos(5x^2-7x(10x-7)) is -sin(5x^2-7x)(10x-7)^2+10cos(5x^2-7x)