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What is the derivative of the quantity 3 times x plus 1 to the one half power?
Take the derivative of (3x+1)1/2First use the power rule on the entire function, then multiply it by the derivative of the inside:(1/2)(3x-1)-1/2(3) = (3/2)(3x-1)-1/2which can also be written as3/(2sqrt(3x-1))(sqrt stands for square root)
What is the derivative of e-3x?
f'(x)=-3the derivative of e is zero because its a constant. Derivative of -3x is -3. Bring the exponent of x down in front of the -3 and subtract the original exponent by 1. Ex. -3(1...which is the first exponent of the x)x^0(n-1 or 1-1=0)all this is -3(1)x^0x^0 is 1 so the derivative of -3x is -3
What is the square root of 24x to the 4th power divided by the square root of 3x?
√(24x)4/√(3x) = [242x2√(3x)]/3x = 8(24)x√(3x) = 192x√(3x)
What is the derivative of 2x2 plus 3x plus 7?
d/dx 2x2+3x+7=4x+3
What is the derivative of 3 divided by square root x?
To find the derivative of ( \frac{3}{\sqrt{x}} ), we can rewrite it as ( 3x^{-\frac{1}{2}} ). Using the power rule, the derivative is ( -\frac{3}{2} x^{-\frac{3}{2}} ). This can also be expressed as ( -\frac{3}{2\sqrt{x^3}} ).
