What is the derivative of (3x-5ye^{2y-4x}) ?

The derivative of (3x-5ye^{2y-4x}) is (3-5(dy)/(dx))e^{2y-4x}+e^{2y-4x}(2(dy)/(dx)-4)(3x-5y)

What is the first derivative of (3x-5ye^{2y-4x}) ?

The first derivative of (3x-5ye^{2y-4x}) is (3-5(dy)/(dx))e^{2y-4x}+e^{2y-4x}(2(dy)/(dx)-4)(3x-5y)

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\frac{d}{d x} ((3 x - 5 y) e^{2 y - 4 x})

(3 - 5 \frac{d y}{d x}) e^{2 y - 4 x} + e^{2 y - 4 x} (2 \frac{d y}{d x} - 4) (3 x - 5 y)

Solution steps

\frac{d}{d x} ((3 x - 5 y) e^{2 y - 4 x})

Apply the Product Rule:

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

f = 3 x - 5 y, g = e^{2 y - 4 x}

= \frac{d}{d x} (3 x - 5 y) e^{2 y - 4 x} + \frac{d}{d x} (e^{2 y - 4 x}) (3 x - 5 y)

\frac{d}{d x} (3 x - 5 y) = 3 - 5 \frac{d y}{d x}

\frac{d}{d x} (e^{2 y - 4 x}) = e^{2 y - 4 x} (2 \frac{d y}{d x} - 4)

= (3 - 5 \frac{d y}{d x}) e^{2 y - 4 x} + e^{2 y - 4 x} (2 \frac{d y}{d x} - 4) (3 x - 5 y)

\int - 3 sin^{2} (x) d x

y = x^{- 5 c o s (x)}

x ln (x) - x

\int \frac{x + 4}{x ^{2} + 6 x - 16} d x

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

What is the derivative of (3x-5ye^{2y-4x}) ?
The derivative of (3x-5ye^{2y-4x}) is (3-5(dy)/(dx))e^{2y-4x}+e^{2y-4x}(2(dy)/(dx)-4)(3x-5y)
What is the first derivative of (3x-5ye^{2y-4x}) ?
The first derivative of (3x-5ye^{2y-4x}) is (3-5(dy)/(dx))e^{2y-4x}+e^{2y-4x}(2(dy)/(dx)-4)(3x-5y)