To find the derivative of the function y=xsinx with respect to x, we will use the product rule of differentiation. The product rule states that if you have two functions u and v, then the derivative of their product is given by: ddx(uv)=udvdx+vdudx 1. Identify the functions: Let...
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Calculate the indicated derivative of the following expression: dydx for sin(x)+sin(y)=xy Implicit Differentiation: We can apply implicit differentiation when we are asked to find the derivative of a variable that is involved in a transcendental equations, o...
A。解析:对于函数\(y = uv\)(这里\(u = x^{2}\),\(v=\sin x\)),根据乘积法则\((uv)^\prime = u^\prime v+uv^\prime\)。\(u = x^{2}\)的导数\(u^\prime = 2x\),\(v=\sin x\)的导数\(v^\prime=\cos x\),所以\(y^\prime = 2x\sin x+x^{2}\cos x\)。选项B中符...
Answer to: Find the derivative, y'(x), of the following: sin(xy) = x - 3. By signing up, you'll get thousands of step-by-step solutions to your...
Derivative of natural logarithm ln x Derivative $f’$ of the function $f(x)=\ln x$ is: \(\forall x \in ]0, +\infty[ , \quad f'(x) = \dfrac{1}{x}\) Proof Let $y$ the function ln x $y = f(x)= \ln x$ then by definition (ln is the inverse function of exp) ...
Here you can see the derivative f'(x) and the second derivative f''(x) of some common functions.Notice how the slope of each function is the y-value of the derivative plotted below it.For example, move to where the sin(x) function slope flattens out (slope=0), then see that the...
Frequently Asked Questions (FAQ) What is the derivative of (3x-y)/x ? The derivative of (3x-y)/x is y/(x^2) What is the first derivative of (3x-y)/x ? The first derivative of (3x-y)/x is y/(x^2)
G(x) = sin(y(x))+cos(y(x)) y(x) Functional Derivative with Respect to Two Functions Copy Code Copy Command Find the functional derivative of the functional S[u,v]=∫ab(u2(x)dv(x)dx+v(x)d2u(x)dx2)dx with respect to the functions u and v, where the integrand is f[u(...
thederivativeofy=f(x). Derivativeformulapage1 axa x x x x aaa ee nxx n a xx xx nn ln 1 )' ln ln ()'(log 1 )'(ln ln)'( )'( )'( 0' 1 Derivativeformulapage2 2 2 2 2 2 2 1 1 )'(arccos 1 1 )'(arcsin csc sin 1 )'(cot sec cos 1 )'(tan sin)'(cos cos)'(...