The derivative with respect to 'x' of sin(pi x) ispi cos(pi x)
I am assuming the you are talking about the graph of the derivative. The graph of the derivative of F(x) is the graph such that, for any x, the value of x on the graph of the derivative of F(x) is the slope at point x in F(x).
the derivative of ln x = x'/x; the derivative of 1 is 0 so the answer is 500(1/x)+0 = 500/x
The derivative of tan(x) is sec2(x).(Which is the same as 1/cos2(x).
1/x = x-1d/dx(x-1) = -x-2 = -1/x2
The first derivative of e to the x power is e to the power of x.
The square root of x = x to the power of a half
f(x)=(pi2)x=pi2x. The derivative of kx=ln(k)*kx, so f'(x)=2ln(pi)*pi2x (with chain rule).
y=x^pid/dx=pi*(x^pi-1)This is true because of power rule.d/dx (x^a)=a(x^(a-1))
-(1/2)X^2 [negative half X squared]
The derivative of 2^x is 2^x * ln2 so the derivative of 2^cosx * ln2 multiplied by d/dx of cox, which is -sinx so the derivative of the inside function is -sinx * 2^cosx *ln2. As to the final question, using the chain rule, d/dx (2^cosx)^0.5 will equal half of (2^cosx)^-0.5 * -sinx * 2^cosx * ln2
The derivative is 2x based on the power rule. Multiply the power by the coefficient of x then drop the power by one.
The derivative, with respect to x, is -x/sqrt(1-x2)
The derivative of ln x is 1/x The derivative of 2ln x is 2(1/x) = 2/x
The derivative of cos(x) is negative sin(x). Also, the derivative of sin(x) is cos(x).
The derivative with respect to 'x' of sin(pi x) ispi cos(pi x)
The derivative of csc(x) is -cot(x)csc(x).