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Popular >

derivative of-e^x+3sqrt(x)-3sin(x)

Solution

derivative of

- e^{x} + 3 x - 3 sin (x)

Solution

- e^{x} + \frac{3}{2 x} - 3 cos (x)

Solution steps

\frac{d}{d x} (- e^{x} + 3 x - 3 sin (x))

Apply the Sum/Difference Rule:

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

= - \frac{d}{d x} (e^{x}) + \frac{d}{d x} (3 x) - \frac{d}{d x} (3 sin (x))

\frac{d}{d x} (e^{x}) = e^{x}

\frac{d}{d x} (3 x) = \frac{3}{2 x}

\frac{d}{d x} (3 sin (x)) = 3 cos (x)

= - e^{x} + \frac{3}{2 x} - 3 cos (x)

Popular Examples

derivative of (sin(x^2+1)^{1/y})

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

(\partial)/(\partial x)(sin(pi(6x-3y)))

\frac{\partial}{\partial x} (sin (π (6 x - 3 y)))

(\partial)/(\partial x)(xy-5x^2y)

\frac{\partial}{\partial x} (x y - 5 x^{2} y)

(d^2)/(dx^2)f(x)=5x^3+12x^2+8x+22

\frac{d ^{2}}{d x ^{2}} f (x) = 5 x^{3} + 12 x^{2} + 8 x + 22

(\partial)/(\partial x)(4(y-1)(x-4)^3)

\frac{\partial}{\partial x} (4 (y - 1) (x - 4)^{3})

Frequently Asked Questions (FAQ)

What is the derivative of-e^x+3sqrt(x)-3sin(x) ?
The derivative of-e^x+3sqrt(x)-3sin(x) is -e^x+3/(2sqrt(x))-3cos(x)
What is the first derivative of-e^x+3sqrt(x)-3sin(x) ?
The first derivative of-e^x+3sqrt(x)-3sin(x) is -e^x+3/(2sqrt(x))-3cos(x)