What is the first derivative of a-bx ?

The first derivative of a-bx is -b

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derivative of a-bx

\frac{d}{d x} (a - b x)

- b

Solution steps

\frac{d}{d x} (a - b x)

Apply the Sum/Difference Rule:

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

= \frac{d a}{d x} - \frac{d}{d x} (b x)

\frac{d a}{d x} = 0

\frac{d}{d x} (b x) = b

= 0 - b

Simplify

= - b

\frac{\partial}{\partial t} (r cos (x))

y^{^{'}} = y (100 - y)

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

x \to 0 lim ((1 + 5 x)^{\frac{4}{x}})

\frac{d y}{d x} - \frac{y}{x} = 3 x e^{x}, y (1) = 3 e - 2