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Popular >

derivative of 16e^{2x}x+32e^{2x}

Solution

\frac{d}{d x} (16 e^{2 x} x + 32 e^{2 x})

Solution

32 e^{2 x} x + 80 e^{2 x}

Solution steps

\frac{d}{d x} (16 e^{2 x} x + 32 e^{2 x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (16 e^{2 x} x) + \frac{d}{d x} (32 e^{2 x})

\frac{d}{d x} (16 e^{2 x} x) = 16 (2 e^{2 x} x + e^{2 x})

\frac{d}{d x} (32 e^{2 x}) = 64 e^{2 x}

= 16 (2 e^{2 x} x + e^{2 x}) + 64 e^{2 x}

Simplify

16 (2 e^{2 x} x + e^{2 x}) + 64 e^{2 x} : 32 e^{2 x} x + 80 e^{2 x}

= 32 e^{2 x} x + 80 e^{2 x}

Popular Examples

(dy)/(dx)=0.08y-100000

\frac{d y}{d x} = 0.08 y - 100000

integral of (sqrt(16x^2-25))/(x^3)

\int \frac{16 x ^{2} - 25}{x ^{3}} d x

derivative of f(x)=sqrt(7x+2)derivative of

f (x) = 7 x + 2

integral of 5/(3x+1)

\int \frac{5}{3 x + 1} d x

y^{''}-8y^'+10y=0,y(0)=0,y^'(0)=5

y^{^{''}} - 8 y^{^{'}} + 10 y = 0, y (0) = 0, y^{^{'}} (0) = 5

Frequently Asked Questions (FAQ)

What is the derivative of 16e^{2x}x+32e^{2x} ?
The derivative of 16e^{2x}x+32e^{2x} is 32e^{2x}x+80e^{2x}
What is the first derivative of 16e^{2x}x+32e^{2x} ?
The first derivative of 16e^{2x}x+32e^{2x} is 32e^{2x}x+80e^{2x}