What is the derivative of (10x-7yi-(7x-2y)j) ?

The derivative of (10x-7yi-(7x-2y)j) is (-7j+2j(dy)/(dx))+i(10-7(dy)/(dx))

What is the first derivative of (10x-7yi-(7x-2y)j) ?

The first derivative of (10x-7yi-(7x-2y)j) is (-7j+2j(dy)/(dx))+i(10-7(dy)/(dx))

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\frac{d}{d x} ((10 x - 7 y) i - (7 x - 2 y) j)

(- 7 j + 2 j \frac{d y}{d x}) + i (10 - 7 \frac{d y}{d x})

Solution steps

\frac{d}{d x} ((10 x - 7 y) i - (7 x - 2 y) j)

Simplify

(10 x - 7 y) i - (7 x - 2 y) j : (- 7 j x + 2 j y (x)) + i (10 x - 7 y)

= \frac{d}{d x} ((- 7 j x + 2 j y (x)) + i (10 x - 7 y))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (- 7 j x + 2 j y (x)) + \frac{d}{d x} (i (10 x - 7 y))

\frac{d}{d x} (- 7 j x + 2 j y (x)) = - 7 j + 2 j \frac{d y}{d x}

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

= - 7 j + 2 j \frac{d y}{d x} + i (10 - 7 \frac{d y}{d x})

Rewrite

- 7 j + 2 j \frac{d y}{d x} + i (10 - 7 \frac{d y}{d x})

in standard complex form:

(- 7 j + 2 j \frac{d y}{d x}) + (10 - 7 \frac{d y}{d x}) i

= (- 7 j + 2 j \frac{d y}{d x}) + i (10 - 7 \frac{d y}{d x})

y = 7 x^{3} + 2 x^{2} + 4 x

\frac{3 y ^{2}}{2}

f (x) = (3 x - 4)^{2} (x - 2)

(x^{2} + 2)^{- 1}

\frac{1}{( 1 + e ^{u} )}

What is the derivative of (10x-7yi-(7x-2y)j) ?
The derivative of (10x-7yi-(7x-2y)j) is (-7j+2j(dy)/(dx))+i(10-7(dy)/(dx))
What is the first derivative of (10x-7yi-(7x-2y)j) ?
The first derivative of (10x-7yi-(7x-2y)j) is (-7j+2j(dy)/(dx))+i(10-7(dy)/(dx))