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Popular Calculus >

derivative of (sin(x+x)^2+7cos(5x))

Solution

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

Solution

2 (sin (x) + x) (cos (x) + 1) - 35 sin (5 x)

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} ((sin (x) + x)^{2}) = 2 (sin (x) + x) (cos (x) + 1)

\frac{d}{d x} (7 cos (5 x)) = - 35 sin (5 x)

= 2 (sin (x) + x) (cos (x) + 1) - 35 sin (5 x)

Graph

Popular Examples

tangent of-(8x)/(x^2+1)

t an g e n t - \frac{8 x}{x ^{2} + 1}

derivative of x^{2/3}*(x-4^2)

\frac{d}{d x} (x^{\frac{2}{3}} \cdot (x - 4)^{2})

integral of (x(sin(x^2)))(cos^8(x^2))

\int (x (sin (x^{2}))) (cos^{8} (x^{2})) d x

derivative of (3x-1^4(-2x+9)^5)

\frac{d}{d x} ((3 x - 1)^{4} (- 2 x + 9)^{5})

y^{''}-7y+10y=0

y^{^{''}} - 7 y + 10 y = 0

Frequently Asked Questions (FAQ)

What is the derivative of (sin(x+x)^2+7cos(5x)) ?
The derivative of (sin(x+x)^2+7cos(5x)) is 2(sin(x)+x)(cos(x)+1)-35sin(5x)
What is the first derivative of (sin(x+x)^2+7cos(5x)) ?
The first derivative of (sin(x+x)^2+7cos(5x)) is 2(sin(x)+x)(cos(x)+1)-35sin(5x)